CIA 1 Life Expectancy
2022-08-14
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## ## Amelia II: Multiple Imputation
## ## (Version 1.8.0, built: 2021-05-26)
## ## Copyright (C) 2005-2022 James Honaker, Gary King and Matthew Blackwell
## ## Refer to http://gking.harvard.edu/amelia/ for more information
## ##library(missRanger)
library(ggplot2)
library(plotly)##
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## layoutImporting the dataset
df <- read.csv(choose.files(), header = T)
head(df)## Country Year Status Life.expectancy Adult.Mortality infant.deaths
## 1 Afghanistan 2015 Developing 65.0 263 62
## 2 Afghanistan 2014 Developing 59.9 271 64
## 3 Afghanistan 2013 Developing 59.9 268 66
## 4 Afghanistan 2012 Developing 59.5 272 69
## 5 Afghanistan 2011 Developing 59.2 275 71
## 6 Afghanistan 2010 Developing 58.8 279 74
## Alcohol percentage.expenditure Hepatitis.B Measles BMI under.five.deaths
## 1 0.01 71.279624 65 1154 19.1 83
## 2 0.01 73.523582 62 492 18.6 86
## 3 0.01 73.219243 64 430 18.1 89
## 4 0.01 78.184215 67 2787 17.6 93
## 5 0.01 7.097109 68 3013 17.2 97
## 6 0.01 79.679367 66 1989 16.7 102
## Polio Total.expenditure Diphtheria HIV.AIDS GDP Population
## 1 6 8.16 65 0.1 584.25921 33736494
## 2 58 8.18 62 0.1 612.69651 327582
## 3 62 8.13 64 0.1 631.74498 31731688
## 4 67 8.52 67 0.1 669.95900 3696958
## 5 68 7.87 68 0.1 63.53723 2978599
## 6 66 9.20 66 0.1 553.32894 2883167
## thinness..1.19.years thinness.5.9.years Income.composition.of.resources
## 1 17.2 17.3 0.479
## 2 17.5 17.5 0.476
## 3 17.7 17.7 0.470
## 4 17.9 18.0 0.463
## 5 18.2 18.2 0.454
## 6 18.4 18.4 0.448
## Schooling
## 1 10.1
## 2 10.0
## 3 9.9
## 4 9.8
## 5 9.5
## 6 9.2Data Preprocessing
Checking the structure of the dataset
str(df)## 'data.frame': 2938 obs. of 22 variables:
## $ Country : chr "Afghanistan" "Afghanistan" "Afghanistan" "Afghanistan" ...
## $ Year : int 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 ...
## $ Status : chr "Developing" "Developing" "Developing" "Developing" ...
## $ Life.expectancy : num 65 59.9 59.9 59.5 59.2 58.8 58.6 58.1 57.5 57.3 ...
## $ Adult.Mortality : int 263 271 268 272 275 279 281 287 295 295 ...
## $ infant.deaths : int 62 64 66 69 71 74 77 80 82 84 ...
## $ Alcohol : num 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.03 0.02 0.03 ...
## $ percentage.expenditure : num 71.3 73.5 73.2 78.2 7.1 ...
## $ Hepatitis.B : int 65 62 64 67 68 66 63 64 63 64 ...
## $ Measles : int 1154 492 430 2787 3013 1989 2861 1599 1141 1990 ...
## $ BMI : num 19.1 18.6 18.1 17.6 17.2 16.7 16.2 15.7 15.2 14.7 ...
## $ under.five.deaths : int 83 86 89 93 97 102 106 110 113 116 ...
## $ Polio : int 6 58 62 67 68 66 63 64 63 58 ...
## $ Total.expenditure : num 8.16 8.18 8.13 8.52 7.87 9.2 9.42 8.33 6.73 7.43 ...
## $ Diphtheria : int 65 62 64 67 68 66 63 64 63 58 ...
## $ HIV.AIDS : num 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 ...
## $ GDP : num 584.3 612.7 631.7 670 63.5 ...
## $ Population : num 33736494 327582 31731688 3696958 2978599 ...
## $ thinness..1.19.years : num 17.2 17.5 17.7 17.9 18.2 18.4 18.6 18.8 19 19.2 ...
## $ thinness.5.9.years : num 17.3 17.5 17.7 18 18.2 18.4 18.7 18.9 19.1 19.3 ...
## $ Income.composition.of.resources: num 0.479 0.476 0.47 0.463 0.454 0.448 0.434 0.433 0.415 0.405 ...
## $ Schooling : num 10.1 10 9.9 9.8 9.5 9.2 8.9 8.7 8.4 8.1 ...Checking for the missing values
sum(is.na(df))## [1] 2563names(which(colSums(is.na(df))>0))## [1] "Life.expectancy" "Adult.Mortality"
## [3] "Alcohol" "Hepatitis.B"
## [5] "BMI" "Polio"
## [7] "Total.expenditure" "Diphtheria"
## [9] "GDP" "Population"
## [11] "thinness..1.19.years" "thinness.5.9.years"
## [13] "Income.composition.of.resources" "Schooling"There are 2563 missing values in 14 different columns.
Imputing the missing values
df_imp <- missRanger(df, pmm.k = 3, seed = 153)##
## Missing value imputation by random forests
##
## Variables to impute: Life.expectancy, Adult.Mortality, Alcohol, Hepatitis.B, BMI, Polio, Total.expenditure, Diphtheria, GDP, Population, thinness..1.19.years, thinness.5.9.years, Income.composition.of.resources, Schooling
## Variables used to impute: Country, Year, Status, Life.expectancy, Adult.Mortality, infant.deaths, Alcohol, percentage.expenditure, Hepatitis.B, Measles, BMI, under.five.deaths, Polio, Total.expenditure, Diphtheria, HIV.AIDS, GDP, Population, thinness..1.19.years, thinness.5.9.years, Income.composition.of.resources, Schooling
## iter 1: ..............
## iter 2: ..............
## iter 3: ..............
## iter 4: ..............head(df_imp)## Country Year Status Life.expectancy Adult.Mortality infant.deaths
## 1 Afghanistan 2015 Developing 65.0 263 62
## 2 Afghanistan 2014 Developing 59.9 271 64
## 3 Afghanistan 2013 Developing 59.9 268 66
## 4 Afghanistan 2012 Developing 59.5 272 69
## 5 Afghanistan 2011 Developing 59.2 275 71
## 6 Afghanistan 2010 Developing 58.8 279 74
## Alcohol percentage.expenditure Hepatitis.B Measles BMI under.five.deaths
## 1 0.01 71.279624 65 1154 19.1 83
## 2 0.01 73.523582 62 492 18.6 86
## 3 0.01 73.219243 64 430 18.1 89
## 4 0.01 78.184215 67 2787 17.6 93
## 5 0.01 7.097109 68 3013 17.2 97
## 6 0.01 79.679367 66 1989 16.7 102
## Polio Total.expenditure Diphtheria HIV.AIDS GDP Population
## 1 6 8.16 65 0.1 584.25921 33736494
## 2 58 8.18 62 0.1 612.69651 327582
## 3 62 8.13 64 0.1 631.74498 31731688
## 4 67 8.52 67 0.1 669.95900 3696958
## 5 68 7.87 68 0.1 63.53723 2978599
## 6 66 9.20 66 0.1 553.32894 2883167
## thinness..1.19.years thinness.5.9.years Income.composition.of.resources
## 1 17.2 17.3 0.479
## 2 17.5 17.5 0.476
## 3 17.7 17.7 0.470
## 4 17.9 18.0 0.463
## 5 18.2 18.2 0.454
## 6 18.4 18.4 0.448
## Schooling
## 1 10.1
## 2 10.0
## 3 9.9
## 4 9.8
## 5 9.5
## 6 9.2range(df_imp$Life.expectancy)## [1] 36.3 89.0sum(is.na(df_imp))## [1] 0Data Cleaning
Creating a new variable with all the columns that are required for the analysis and model building.
Removing “Country” and “Year”, because it has too many variables and time series which doesn’t really help in predicting life expectancy.
Using another variable for Categorical Analysis
life_selected <- df_imp %>%
mutate(Hepatitis.B = ifelse(Hepatitis.B < 90, "<90% Covered", ">=90% Covered"),
Polio = ifelse(Polio < 90, "<90% Covered", ">=90% Covered"),
Diphtheria = ifelse(Diphtheria < 90, "<90% Covered", ">=90% Covered"),
Hepatitis.B = as.factor(Hepatitis.B),
Polio = as.factor(Polio),
Diphtheria = as.factor(Diphtheria))
life_selected$Country <- NULL
life_selected$Year <- NULL
str(life_selected)## 'data.frame': 2938 obs. of 20 variables:
## $ Status : chr "Developing" "Developing" "Developing" "Developing" ...
## $ Life.expectancy : num 65 59.9 59.9 59.5 59.2 58.8 58.6 58.1 57.5 57.3 ...
## $ Adult.Mortality : int 263 271 268 272 275 279 281 287 295 295 ...
## $ infant.deaths : int 62 64 66 69 71 74 77 80 82 84 ...
## $ Alcohol : num 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.03 0.02 0.03 ...
## $ percentage.expenditure : num 71.3 73.5 73.2 78.2 7.1 ...
## $ Hepatitis.B : Factor w/ 2 levels "<90% Covered",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ Measles : int 1154 492 430 2787 3013 1989 2861 1599 1141 1990 ...
## $ BMI : num 19.1 18.6 18.1 17.6 17.2 16.7 16.2 15.7 15.2 14.7 ...
## $ under.five.deaths : int 83 86 89 93 97 102 106 110 113 116 ...
## $ Polio : Factor w/ 2 levels "<90% Covered",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ Total.expenditure : num 8.16 8.18 8.13 8.52 7.87 9.2 9.42 8.33 6.73 7.43 ...
## $ Diphtheria : Factor w/ 2 levels "<90% Covered",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ HIV.AIDS : num 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 ...
## $ GDP : num 584.3 612.7 631.7 670 63.5 ...
## $ Population : num 33736494 327582 31731688 3696958 2978599 ...
## $ thinness..1.19.years : num 17.2 17.5 17.7 17.9 18.2 18.4 18.6 18.8 19 19.2 ...
## $ thinness.5.9.years : num 17.3 17.5 17.7 18 18.2 18.4 18.7 18.9 19.1 19.3 ...
## $ Income.composition.of.resources: num 0.479 0.476 0.47 0.463 0.454 0.448 0.434 0.433 0.415 0.405 ...
## $ Schooling : num 10.1 10 9.9 9.8 9.5 9.2 8.9 8.7 8.4 8.1 ...life_selected$Status <- as.factor(life_selected$Status)
str(life_selected)## 'data.frame': 2938 obs. of 20 variables:
## $ Status : Factor w/ 2 levels "Developed","Developing": 2 2 2 2 2 2 2 2 2 2 ...
## $ Life.expectancy : num 65 59.9 59.9 59.5 59.2 58.8 58.6 58.1 57.5 57.3 ...
## $ Adult.Mortality : int 263 271 268 272 275 279 281 287 295 295 ...
## $ infant.deaths : int 62 64 66 69 71 74 77 80 82 84 ...
## $ Alcohol : num 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.03 0.02 0.03 ...
## $ percentage.expenditure : num 71.3 73.5 73.2 78.2 7.1 ...
## $ Hepatitis.B : Factor w/ 2 levels "<90% Covered",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ Measles : int 1154 492 430 2787 3013 1989 2861 1599 1141 1990 ...
## $ BMI : num 19.1 18.6 18.1 17.6 17.2 16.7 16.2 15.7 15.2 14.7 ...
## $ under.five.deaths : int 83 86 89 93 97 102 106 110 113 116 ...
## $ Polio : Factor w/ 2 levels "<90% Covered",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ Total.expenditure : num 8.16 8.18 8.13 8.52 7.87 9.2 9.42 8.33 6.73 7.43 ...
## $ Diphtheria : Factor w/ 2 levels "<90% Covered",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ HIV.AIDS : num 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 ...
## $ GDP : num 584.3 612.7 631.7 670 63.5 ...
## $ Population : num 33736494 327582 31731688 3696958 2978599 ...
## $ thinness..1.19.years : num 17.2 17.5 17.7 17.9 18.2 18.4 18.6 18.8 19 19.2 ...
## $ thinness.5.9.years : num 17.3 17.5 17.7 18 18.2 18.4 18.7 18.9 19.1 19.3 ...
## $ Income.composition.of.resources: num 0.479 0.476 0.47 0.463 0.454 0.448 0.434 0.433 0.415 0.405 ...
## $ Schooling : num 10.1 10 9.9 9.8 9.5 9.2 8.9 8.7 8.4 8.1 ...Exploratory Data Analysis
Categorical Variables
Checking the data distribution of Life.expectancy among all of the Categorical Variables
Status
life_selected %>%
group_by(Status) %>%
summarise(count = n()) %>%
mutate(percentage = paste0(round(count/sum(count)*100, 2), "%"))## # A tibble: 2 x 3
## Status count percentage
## <fct> <int> <chr>
## 1 Developed 512 17.43%
## 2 Developing 2426 82.57%plot1 <- ggplot(life_selected, aes(x=Status, y = Life.expectancy, fill = Status)) +
geom_boxplot() +
scale_fill_manual(values=c("green3", "darkorange")) +
labs(x = "Development Status", y = "Life Expectancy (Age)") +
theme(legend.position = "none")
ggplotly(plot1)summary(aov(Life.expectancy ~ Status, data = life_selected))## Df Sum Sq Mean Sq F value Pr(>F)
## Status 1 61418 61418 881.8 <2e-16 ***
## Residuals 2936 204499 70
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1- The number of developing nations is significantly higher than the number of developed nations in these observations.
- According to the Development Status, it was evident that the Developed Countries have a greater Life Expectancy Distribution, with a Significant Median Distance. Additionally, even though there are some developing country outliers, we will keep them for the time being because they have low leverage.
- We can infer that there are substantial disparities in life expectancy between developed and developing countries because the p-value from the ANOVA analysis is less than the significance level of 0.05.
Hepatitis B Coverage
life_selected %>%
group_by(Hepatitis.B) %>%
summarise(count = n()) %>%
mutate(percentage = paste0(round(count/sum(count)*100, 2), "%"))## # A tibble: 2 x 3
## Hepatitis.B count percentage
## <fct> <int> <chr>
## 1 <90% Covered 1504 51.19%
## 2 >=90% Covered 1434 48.81%plot2 <- ggplot(life_selected, aes(x=Hepatitis.B, y = Life.expectancy, fill = Hepatitis.B)) +
geom_boxplot() +
scale_fill_manual(values=c("green3", "darkorange")) +
labs(x = "Hepatitis B Coverage", y = "Life Expectancy (Age)") +
theme(legend.position = "none")
ggplotly(plot2)summary(aov(Life.expectancy ~ Hepatitis.B, data = life_selected))## Df Sum Sq Mean Sq F value Pr(>F)
## Hepatitis.B 1 41593 41593 544.4 <2e-16 ***
## Residuals 2936 224324 76
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1- Surprisingly, half of the findings are from countries where hepatitis.B vaccination coverage is less than 90%.
- Greater life expectancy is associated with countries that cover their hepatitis B vaccination at a rate of 90% or higher, with a significant median gap. Even though there are few outliers among the developing nations, the majority of them have low leverage, so we will preserve it for the time being.
- We can infer that there are significant differences in Life Expectancy across the groups in Hepatitis B Coverage because the p-value is less than the significance level of 0.05.
Polio Coverage
life_selected %>%
group_by(Polio) %>%
summarise(count = n()) %>%
mutate(percentage = paste0(round(count/sum(count)*100, 2), "%"))## # A tibble: 2 x 3
## Polio count percentage
## <fct> <int> <chr>
## 1 <90% Covered 1248 42.48%
## 2 >=90% Covered 1690 57.52%plot3 <- ggplot(life_selected, aes(x=Polio, y = Life.expectancy, fill = Polio)) +
geom_boxplot() +
scale_fill_manual(values=c("green3", "darkorange")) +
labs(x = "Polio Coverage", y = "Life Expectancy (Age)") +
theme(legend.position = "none")
ggplotly(plot3)summary(aov(Life.expectancy ~ Polio, data = life_selected))## Df Sum Sq Mean Sq F value Pr(>F)
## Polio 1 85316 85316 1387 <2e-16 ***
## Residuals 2936 180600 62
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1- Greater Polio Coverage is better than Hepatitis B Coverage.
- Greater life expectancy is associated with countries that have polio vaccination coverage rates of 90% or higher, with a significant median distance. Polio does not have the same high outliers as Hepatitis.B. Even though there are few outliers among the developing nations, the majority of them have low leverage, so we will preserve it for the time being.
- We can draw the conclusion that there are significant differences in life expectancy between the groups in polio coverage because the p-value of the ANOVA Analysis is less than the significance level of 0.05.
Diphteria
life_selected %>%
group_by(Diphtheria) %>%
summarise(count = n()) %>%
mutate(percentage = paste0(round(count/sum(count)*100, 2), "%"))## # A tibble: 2 x 3
## Diphtheria count percentage
## <fct> <int> <chr>
## 1 <90% Covered 1262 42.95%
## 2 >=90% Covered 1676 57.05%plot4 <- ggplot(life_selected, aes(x=Diphtheria, y = Life.expectancy, fill = Diphtheria)) +
geom_boxplot() +
scale_fill_manual(values=c("green3", "darkorange")) +
labs(x = "Diphtheria Coverage", y = "Life Expectancy (Age)") +
theme(legend.position = "none")
ggplotly(plot4)summary(aov(Life.expectancy ~ Diphtheria, data = life_selected))## Df Sum Sq Mean Sq F value Pr(>F)
## Diphtheria 1 85302 85302 1387 <2e-16 ***
## Residuals 2936 180615 62
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1- In terms of the number of countries, diphtheria coverage is comparable to polio coverage.
- The spread of diphtheria and polio are somewhat comparable. It can mean that Diphtheria and Polio vaccinations are administered simultaneously.
- We can draw the conclusion that there are significant differences in life expectancy between the groups in diphtheria coverage because the p-value of the ANOVA Analysis is less than the significance level of 0.05.
Association between Categorical Variables
Development Status vs Hepatitis B Coverage
library(ggmosaic)
plot5 <- ggplot(life_selected) +
geom_mosaic(aes(x = product(Status), fill=Hepatitis.B)) +
labs(x = NULL, y = NULL) +
scale_fill_manual(values=c("green3", "darkorange")) +
theme(legend.position = "none")
ggplotly(plot5) ## Warning: `unite_()` was deprecated in tidyr 1.2.0.
## Please use `unite()` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was generated.chisq.test(table(life_selected$Status, life_selected$Hepatitis.B))##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: table(life_selected$Status, life_selected$Hepatitis.B)
## X-squared = 54.105, df = 1, p-value = 1.901e-13- The majority of developed nations have higher vaccination rates for hepatitis B.
- By using the chi-square test, we can see compelling evidence that developed and developing countries typically have different coverage rates for the hepatitis.B vaccine.
Development Status vs Polio Coverage
plot6 <- ggplot(life_selected) +
geom_mosaic(aes(x = product(Status), fill=Polio)) +
labs(x = NULL, y = NULL) +
scale_fill_manual(values=c("green3", "darkorange")) +
theme(legend.position = "none")
ggplotly(plot6) chisq.test(table(life_selected$Status, life_selected$Polio))##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: table(life_selected$Status, life_selected$Polio)
## X-squared = 269.93, df = 1, p-value < 2.2e-16- Developed nations have much higher inoculation rates against polio
- By using the chi-square test, we can observe compelling evidence that developed and developing countries typically have different vaccine coverage rates for polio.
Development Status vs Diphtheria Coverage
plot7 <- ggplot(life_selected) +
geom_mosaic(aes(x = product(Status), fill=Diphtheria)) +
labs(x = NULL, y = NULL) +
scale_fill_manual(values=c("green3", "darkorange")) +
theme(legend.position = "none")
ggplotly(plot7) chisq.test(table(life_selected$Status, life_selected$Diphtheria))##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: table(life_selected$Status, life_selected$Diphtheria)
## X-squared = 286.99, df = 1, p-value < 2.2e-16- The relationship between Diphtheria and Polio is comparable to earlier discoveries. On the following test, we’ll determine if we just require one of them.
Using the dataframe to split the categorical variables to numerical variables
life_exp <- df_imp
life_exp$Developed <- ifelse(life_exp$Status == "Developed", 1, 0)
life_exp$Developing <- ifelse(life_exp$Status == "Developing", 1, 0)
life_exp$Hepatitis.B_below90 <- ifelse(life_exp$Hepatitis.B < 90, 1, 0)
life_exp$Hepatitis.B_above90 <- ifelse(life_exp$Hepatitis.B >= 90, 1, 0)
life_exp$Polio_below90 <- ifelse(life_exp$Polio < 90, 1, 0)
life_exp$Polio_above90 <- ifelse(life_exp$Polio >= 90, 1, 0)
life_exp$Diphtheria_below90 <- ifelse(life_exp$Diphtheria < 90, 1, 0)
life_exp$Diphtheria_above90 <- ifelse(life_exp$Diphtheria >= 90, 1, 0)Dropping the Unwanted columns
life_exp <- life_exp[c(4:6, 10:12, 14, 16:30)]
head(life_exp)## Life.expectancy Adult.Mortality infant.deaths Measles BMI under.five.deaths
## 1 65.0 263 62 1154 19.1 83
## 2 59.9 271 64 492 18.6 86
## 3 59.9 268 66 430 18.1 89
## 4 59.5 272 69 2787 17.6 93
## 5 59.2 275 71 3013 17.2 97
## 6 58.8 279 74 1989 16.7 102
## Total.expenditure HIV.AIDS GDP Population thinness..1.19.years
## 1 8.16 0.1 584.25921 33736494 17.2
## 2 8.18 0.1 612.69651 327582 17.5
## 3 8.13 0.1 631.74498 31731688 17.7
## 4 8.52 0.1 669.95900 3696958 17.9
## 5 7.87 0.1 63.53723 2978599 18.2
## 6 9.20 0.1 553.32894 2883167 18.4
## thinness.5.9.years Income.composition.of.resources Schooling Developed
## 1 17.3 0.479 10.1 0
## 2 17.5 0.476 10.0 0
## 3 17.7 0.470 9.9 0
## 4 18.0 0.463 9.8 0
## 5 18.2 0.454 9.5 0
## 6 18.4 0.448 9.2 0
## Developing Hepatitis.B_below90 Hepatitis.B_above90 Polio_below90
## 1 1 1 0 1
## 2 1 1 0 1
## 3 1 1 0 1
## 4 1 1 0 1
## 5 1 1 0 1
## 6 1 1 0 1
## Polio_above90 Diphtheria_below90 Diphtheria_above90
## 1 0 1 0
## 2 0 1 0
## 3 0 1 0
## 4 0 1 0
## 5 0 1 0
## 6 0 1 0str(life_exp)## 'data.frame': 2938 obs. of 22 variables:
## $ Life.expectancy : num 65 59.9 59.9 59.5 59.2 58.8 58.6 58.1 57.5 57.3 ...
## $ Adult.Mortality : int 263 271 268 272 275 279 281 287 295 295 ...
## $ infant.deaths : int 62 64 66 69 71 74 77 80 82 84 ...
## $ Measles : int 1154 492 430 2787 3013 1989 2861 1599 1141 1990 ...
## $ BMI : num 19.1 18.6 18.1 17.6 17.2 16.7 16.2 15.7 15.2 14.7 ...
## $ under.five.deaths : int 83 86 89 93 97 102 106 110 113 116 ...
## $ Total.expenditure : num 8.16 8.18 8.13 8.52 7.87 9.2 9.42 8.33 6.73 7.43 ...
## $ HIV.AIDS : num 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 ...
## $ GDP : num 584.3 612.7 631.7 670 63.5 ...
## $ Population : num 33736494 327582 31731688 3696958 2978599 ...
## $ thinness..1.19.years : num 17.2 17.5 17.7 17.9 18.2 18.4 18.6 18.8 19 19.2 ...
## $ thinness.5.9.years : num 17.3 17.5 17.7 18 18.2 18.4 18.7 18.9 19.1 19.3 ...
## $ Income.composition.of.resources: num 0.479 0.476 0.47 0.463 0.454 0.448 0.434 0.433 0.415 0.405 ...
## $ Schooling : num 10.1 10 9.9 9.8 9.5 9.2 8.9 8.7 8.4 8.1 ...
## $ Developed : num 0 0 0 0 0 0 0 0 0 0 ...
## $ Developing : num 1 1 1 1 1 1 1 1 1 1 ...
## $ Hepatitis.B_below90 : num 1 1 1 1 1 1 1 1 1 1 ...
## $ Hepatitis.B_above90 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ Polio_below90 : num 1 1 1 1 1 1 1 1 1 1 ...
## $ Polio_above90 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ Diphtheria_below90 : num 1 1 1 1 1 1 1 1 1 1 ...
## $ Diphtheria_above90 : num 0 0 0 0 0 0 0 0 0 0 ...Correlation
life_cor <- cor(life_exp)
life_cor## Life.expectancy Adult.Mortality infant.deaths
## Life.expectancy 1.00000000 -0.696626466 -0.19692975
## Adult.Mortality -0.69662647 1.000000000 0.07931261
## infant.deaths -0.19692975 0.079312611 1.00000000
## Measles -0.15790099 0.031673459 0.50112834
## BMI 0.57134224 -0.393065148 -0.22758957
## under.five.deaths -0.22288775 0.094697101 0.99662888
## Total.expenditure 0.23044622 -0.127919303 -0.13102225
## HIV.AIDS -0.55670595 0.523993429 0.02523132
## GDP 0.44917692 -0.295235102 -0.10642924
## Population -0.03294244 -0.001989446 0.55726765
## thinness..1.19.years -0.48047136 0.307818627 0.46469284
## thinness.5.9.years -0.47437834 0.312750080 0.47038449
## Income.composition.of.resources 0.73649241 -0.474912519 -0.16470019
## Schooling 0.76208016 -0.472390497 -0.21271968
## Developed 0.48058927 -0.313682017 -0.11225158
## Developing -0.48058927 0.313682017 0.11225158
## Hepatitis.B_below90 -0.39549144 0.262109092 0.17495190
## Hepatitis.B_above90 0.39549144 -0.262109092 -0.17495190
## Polio_below90 -0.56642658 0.366536927 0.21411536
## Polio_above90 0.56642658 -0.366536927 -0.21411536
## Diphtheria_below90 -0.56637789 0.363056541 0.21238743
## Diphtheria_above90 0.56637789 -0.363056541 -0.21238743
## Measles BMI under.five.deaths
## Life.expectancy -0.15790099 0.57134224 -0.22288775
## Adult.Mortality 0.03167346 -0.39306515 0.09469710
## infant.deaths 0.50112834 -0.22758957 0.99662888
## Measles 1.00000000 -0.17426596 0.50780871
## BMI -0.17426596 1.00000000 -0.23834974
## under.five.deaths 0.50780871 -0.23834974 1.00000000
## Total.expenditure -0.10698225 0.25450586 -0.13265932
## HIV.AIDS 0.03089872 -0.24243839 0.03806151
## GDP -0.07355282 0.29406686 -0.10999641
## Population 0.26715586 -0.06966492 0.54491457
## thinness..1.19.years 0.22349730 -0.53560160 0.46715303
## thinness.5.9.years 0.21990855 -0.54218736 0.47168144
## Income.composition.of.resources -0.15351757 0.52084467 -0.18385354
## Schooling -0.16526449 0.56066078 -0.22954523
## Developed -0.07695507 0.31377031 -0.11519509
## Developing 0.07695507 -0.31377031 0.11519509
## Hepatitis.B_below90 0.12264181 -0.23793027 0.18566031
## Hepatitis.B_above90 -0.12264181 0.23793027 -0.18566031
## Polio_below90 0.15136310 -0.33780111 0.22620022
## Polio_above90 -0.15136310 0.33780111 -0.22620022
## Diphtheria_below90 0.14053796 -0.33316029 0.22474158
## Diphtheria_above90 -0.14053796 0.33316029 -0.22474158
## Total.expenditure HIV.AIDS GDP
## Life.expectancy 0.230446220 -0.556705954 0.44917692
## Adult.Mortality -0.127919303 0.523993429 -0.29523510
## infant.deaths -0.131022249 0.025231318 -0.10642924
## Measles -0.106982247 0.030898718 -0.07355282
## BMI 0.254505864 -0.242438392 0.29406686
## under.five.deaths -0.132659321 0.038061512 -0.10999641
## Total.expenditure 1.000000000 -0.005493024 0.14162395
## HIV.AIDS -0.005493024 1.000000000 -0.12760549
## GDP 0.141623948 -0.127605489 1.00000000
## Population -0.057854707 -0.020012844 -0.03156714
## thinness..1.19.years -0.290820063 0.201795799 -0.28173976
## thinness.5.9.years -0.297970679 0.204798392 -0.28534864
## Income.composition.of.resources 0.205988337 -0.254746613 0.44637038
## Schooling 0.287997527 -0.225945962 0.43825108
## Developed 0.307915267 -0.148590059 0.46668560
## Developing -0.307915267 0.148590059 -0.46668560
## Hepatitis.B_below90 -0.086237946 0.197129865 -0.09988033
## Hepatitis.B_above90 0.086237946 -0.197129865 0.09988033
## Polio_below90 -0.155435726 0.270937717 -0.26859744
## Polio_above90 0.155435726 -0.270937717 0.26859744
## Diphtheria_below90 -0.176127349 0.263485357 -0.27212187
## Diphtheria_above90 0.176127349 -0.263485357 0.27212187
## Population thinness..1.19.years
## Life.expectancy -0.032942445 -0.4804714
## Adult.Mortality -0.001989446 0.3078186
## infant.deaths 0.557267650 0.4646928
## Measles 0.267155857 0.2234973
## BMI -0.069664918 -0.5356016
## under.five.deaths 0.544914569 0.4671530
## Total.expenditure -0.057854707 -0.2908201
## HIV.AIDS -0.020012844 0.2017958
## GDP -0.031567137 -0.2817398
## Population 1.000000000 0.2427012
## thinness..1.19.years 0.242701227 1.0000000
## thinness.5.9.years 0.240939542 0.9398249
## Income.composition.of.resources -0.020035719 -0.4378224
## Schooling -0.041171199 -0.4851424
## Developed -0.038613476 -0.3695766
## Developing 0.038613476 0.3695766
## Hepatitis.B_below90 0.063201193 0.1721079
## Hepatitis.B_above90 -0.063201193 -0.1721079
## Polio_below90 0.070275553 0.2731081
## Polio_above90 -0.070275553 -0.2731081
## Diphtheria_below90 0.066990489 0.2800136
## Diphtheria_above90 -0.066990489 -0.2800136
## thinness.5.9.years
## Life.expectancy -0.4743783
## Adult.Mortality 0.3127501
## infant.deaths 0.4703845
## Measles 0.2199085
## BMI -0.5421874
## under.five.deaths 0.4716814
## Total.expenditure -0.2979707
## HIV.AIDS 0.2047984
## GDP -0.2853486
## Population 0.2409395
## thinness..1.19.years 0.9398249
## thinness.5.9.years 1.0000000
## Income.composition.of.resources -0.4267865
## Schooling -0.4730321
## Developed -0.3678503
## Developing 0.3678503
## Hepatitis.B_below90 0.1822763
## Hepatitis.B_above90 -0.1822763
## Polio_below90 0.2863211
## Polio_above90 -0.2863211
## Diphtheria_below90 0.2946470
## Diphtheria_above90 -0.2946470
## Income.composition.of.resources Schooling
## Life.expectancy 0.73649241 0.7620802
## Adult.Mortality -0.47491252 -0.4723905
## infant.deaths -0.16470019 -0.2127197
## Measles -0.15351757 -0.1652645
## BMI 0.52084467 0.5606608
## under.five.deaths -0.18385354 -0.2295452
## Total.expenditure 0.20598834 0.2879975
## HIV.AIDS -0.25474661 -0.2259460
## GDP 0.44637038 0.4382511
## Population -0.02003572 -0.0411712
## thinness..1.19.years -0.43782239 -0.4851424
## thinness.5.9.years -0.42678654 -0.4730321
## Income.composition.of.resources 1.00000000 0.8108359
## Schooling 0.81083588 1.0000000
## Developed 0.48691956 0.5257973
## Developing -0.48691956 -0.5257973
## Hepatitis.B_below90 -0.32977993 -0.3600401
## Hepatitis.B_above90 0.32977993 0.3600401
## Polio_below90 -0.47586703 -0.5182907
## Polio_above90 0.47586703 0.5182907
## Diphtheria_below90 -0.48667960 -0.5281486
## Diphtheria_above90 0.48667960 0.5281486
## Developed Developing Hepatitis.B_below90
## Life.expectancy 0.48058927 -0.48058927 -0.39549144
## Adult.Mortality -0.31368202 0.31368202 0.26210909
## infant.deaths -0.11225158 0.11225158 0.17495190
## Measles -0.07695507 0.07695507 0.12264181
## BMI 0.31377031 -0.31377031 -0.23793027
## under.five.deaths -0.11519509 0.11519509 0.18566031
## Total.expenditure 0.30791527 -0.30791527 -0.08623795
## HIV.AIDS -0.14859006 0.14859006 0.19712986
## GDP 0.46668560 -0.46668560 -0.09988033
## Population -0.03861348 0.03861348 0.06320119
## thinness..1.19.years -0.36957657 0.36957657 0.17210792
## thinness.5.9.years -0.36785032 0.36785032 0.18227633
## Income.composition.of.resources 0.48691956 -0.48691956 -0.32977993
## Schooling 0.52579729 -0.52579729 -0.36004008
## Developed 1.00000000 -1.00000000 -0.13660106
## Developing -1.00000000 1.00000000 0.13660106
## Hepatitis.B_below90 -0.13660106 0.13660106 1.00000000
## Hepatitis.B_above90 0.13660106 -0.13660106 -1.00000000
## Polio_below90 -0.30401930 0.30401930 0.75920466
## Polio_above90 0.30401930 -0.30401930 -0.75920466
## Diphtheria_below90 -0.31344853 0.31344853 0.78541073
## Diphtheria_above90 0.31344853 -0.31344853 -0.78541073
## Hepatitis.B_above90 Polio_below90 Polio_above90
## Life.expectancy 0.39549144 -0.56642658 0.56642658
## Adult.Mortality -0.26210909 0.36653693 -0.36653693
## infant.deaths -0.17495190 0.21411536 -0.21411536
## Measles -0.12264181 0.15136310 -0.15136310
## BMI 0.23793027 -0.33780111 0.33780111
## under.five.deaths -0.18566031 0.22620022 -0.22620022
## Total.expenditure 0.08623795 -0.15543573 0.15543573
## HIV.AIDS -0.19712986 0.27093772 -0.27093772
## GDP 0.09988033 -0.26859744 0.26859744
## Population -0.06320119 0.07027555 -0.07027555
## thinness..1.19.years -0.17210792 0.27310810 -0.27310810
## thinness.5.9.years -0.18227633 0.28632107 -0.28632107
## Income.composition.of.resources 0.32977993 -0.47586703 0.47586703
## Schooling 0.36004008 -0.51829067 0.51829067
## Developed 0.13660106 -0.30401930 0.30401930
## Developing -0.13660106 0.30401930 -0.30401930
## Hepatitis.B_below90 -1.00000000 0.75920466 -0.75920466
## Hepatitis.B_above90 1.00000000 -0.75920466 0.75920466
## Polio_below90 -0.75920466 1.00000000 -1.00000000
## Polio_above90 0.75920466 -1.00000000 1.00000000
## Diphtheria_below90 -0.78541073 0.91241293 -0.91241293
## Diphtheria_above90 0.78541073 -0.91241293 0.91241293
## Diphtheria_below90 Diphtheria_above90
## Life.expectancy -0.56637789 0.56637789
## Adult.Mortality 0.36305654 -0.36305654
## infant.deaths 0.21238743 -0.21238743
## Measles 0.14053796 -0.14053796
## BMI -0.33316029 0.33316029
## under.five.deaths 0.22474158 -0.22474158
## Total.expenditure -0.17612735 0.17612735
## HIV.AIDS 0.26348536 -0.26348536
## GDP -0.27212187 0.27212187
## Population 0.06699049 -0.06699049
## thinness..1.19.years 0.28001364 -0.28001364
## thinness.5.9.years 0.29464704 -0.29464704
## Income.composition.of.resources -0.48667960 0.48667960
## Schooling -0.52814865 0.52814865
## Developed -0.31344853 0.31344853
## Developing 0.31344853 -0.31344853
## Hepatitis.B_below90 0.78541073 -0.78541073
## Hepatitis.B_above90 -0.78541073 0.78541073
## Polio_below90 0.91241293 -0.91241293
## Polio_above90 -0.91241293 0.91241293
## Diphtheria_below90 1.00000000 -1.00000000
## Diphtheria_above90 -1.00000000 1.00000000library(corrplot)## corrplot 0.92 loadedcorrplot(life_cor, method = "number", addCoef.col = "black",number.cex=0.50)
Since it is hard to interpret, plotting correlation using ggcorr.
library(GGally)## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2##
## Attaching package: 'GGally'## The following object is masked from 'package:ggmosaic':
##
## happydata_num <- life_exp %>%
select_if(is.numeric)
ggcorr(data_num,
label = T,
label_size = 2,
label_round = 2,
hjust = 1,
size = 3,
color = "royalblue",
layout.exp = 5,
low = "green3",
mid = "gray95",
high = "darkorange",
name = "Correlation")
In the model analysis, we will see that the dependent variable, Life Expectancy, has a moderately strong positive correlation with the independent variables, Education, and Income Composition of Resources. However, there is a bad link between it and adult mortality. This is a true fact, as a high adult mortality rate will inevitably result in a poor life expectancy for all.
A very little link exists between life expectancy and both the population and the measles. The following analysis will be used to evaluate it further.
Additionally, the Corr Matrix reveals a very significant link between baby deaths and under-five fatalities. This high correlation suggests that there is multicollinearity between them. Since other factors appear to be more closely related to situations during the neonatal period, we will deselect under 5.deaths.
life_exp1 <- life_exp %>%
select(-under.five.deaths)
head(life_exp1)## Life.expectancy Adult.Mortality infant.deaths Measles BMI Total.expenditure
## 1 65.0 263 62 1154 19.1 8.16
## 2 59.9 271 64 492 18.6 8.18
## 3 59.9 268 66 430 18.1 8.13
## 4 59.5 272 69 2787 17.6 8.52
## 5 59.2 275 71 3013 17.2 7.87
## 6 58.8 279 74 1989 16.7 9.20
## HIV.AIDS GDP Population thinness..1.19.years thinness.5.9.years
## 1 0.1 584.25921 33736494 17.2 17.3
## 2 0.1 612.69651 327582 17.5 17.5
## 3 0.1 631.74498 31731688 17.7 17.7
## 4 0.1 669.95900 3696958 17.9 18.0
## 5 0.1 63.53723 2978599 18.2 18.2
## 6 0.1 553.32894 2883167 18.4 18.4
## Income.composition.of.resources Schooling Developed Developing
## 1 0.479 10.1 0 1
## 2 0.476 10.0 0 1
## 3 0.470 9.9 0 1
## 4 0.463 9.8 0 1
## 5 0.454 9.5 0 1
## 6 0.448 9.2 0 1
## Hepatitis.B_below90 Hepatitis.B_above90 Polio_below90 Polio_above90
## 1 1 0 1 0
## 2 1 0 1 0
## 3 1 0 1 0
## 4 1 0 1 0
## 5 1 0 1 0
## 6 1 0 1 0
## Diphtheria_below90 Diphtheria_above90
## 1 1 0
## 2 1 0
## 3 1 0
## 4 1 0
## 5 1 0
## 6 1 0Model Building
As was said at the outset of this Analysis, we’ll use a few key variables to forecast life expectancy. The complete linear prediction model is presented here.
Model1 <- lm(formula = Life.expectancy ~ ., data = life_exp1)
summary(Model1)##
## Call:
## lm(formula = Life.expectancy ~ ., data = life_exp1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -21.2891 -2.2731 0.0099 2.3397 18.8170
##
## Coefficients: (4 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.817e+01 5.358e-01 108.566 < 2e-16 ***
## Adult.Mortality -1.786e-02 7.917e-04 -22.561 < 2e-16 ***
## infant.deaths -1.007e-03 9.242e-04 -1.090 0.27587
## Measles -1.756e-05 7.524e-06 -2.334 0.01964 *
## BMI 3.709e-02 4.927e-03 7.528 6.80e-14 ***
## Total.expenditure 5.264e-02 3.254e-02 1.618 0.10581
## HIV.AIDS -4.806e-01 1.741e-02 -27.608 < 2e-16 ***
## GDP 4.715e-05 6.637e-06 7.104 1.52e-12 ***
## Population 2.389e-09 1.638e-09 1.458 0.14488
## thinness..1.19.years -1.251e-01 4.973e-02 -2.515 0.01194 *
## thinness.5.9.years 6.262e-02 4.902e-02 1.278 0.20150
## Income.composition.of.resources 7.463e+00 6.185e-01 12.067 < 2e-16 ***
## Schooling 7.797e-01 4.126e-02 18.898 < 2e-16 ***
## Developed 6.764e-01 2.503e-01 2.703 0.00692 **
## Developing NA NA NA NA
## Hepatitis.B_below90 3.184e-01 2.497e-01 1.275 0.20246
## Hepatitis.B_above90 NA NA NA NA
## Polio_below90 -1.515e+00 3.755e-01 -4.035 5.60e-05 ***
## Polio_above90 NA NA NA NA
## Diphtheria_below90 -1.110e+00 3.997e-01 -2.776 0.00554 **
## Diphtheria_above90 NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.003 on 2921 degrees of freedom
## Multiple R-squared: 0.824, Adjusted R-squared: 0.8231
## F-statistic: 854.8 on 16 and 2921 DF, p-value: < 2.2e-16- Interpretation of coefficients: Since there is no condition when all of the independent variables are 0, the intercept is irrelevant in this situation. The coefficients reveal some intriguing results; several of the numerical variables, like adult mortality, infant mortality, alcohol use, HIV infection, and thinness, may have detrimental consequences. Additional of these Variables, according to 10 19.years, may result in a decrease in life expectancy. On the other side, the Life.expectancy is greatly influenced by the Income.composition.of.Resources.
- Adj. R-squared interpretation: This is a positive result, showing that we are on the right track to develop a good linear model. Approximately 82.40% of the observed variation can be explained by the model’s inputs.
- The most significant predictors, as shown by the p-value, are adult mortality, alcohol use, BMI, HIV/AIDS, income composition of resources, and education. Measles came in second with a 0.01 significant level. For the other variables, we may assume that changes in those predictors do not significantly affect life expectancy.
Advanced Feature Selection
We will now choose the most crucial predictors using R’s automatic calculation.
Backward Direction
model_backward <- stepAIC(Model1, direction = "backward")## Start: AIC=8166.65
## Life.expectancy ~ Adult.Mortality + infant.deaths + Measles +
## BMI + Total.expenditure + HIV.AIDS + GDP + Population + thinness..1.19.years +
## thinness.5.9.years + Income.composition.of.resources + Schooling +
## Developed + Developing + Hepatitis.B_below90 + Hepatitis.B_above90 +
## Polio_below90 + Polio_above90 + Diphtheria_below90 + Diphtheria_above90
##
##
## Step: AIC=8166.65
## Life.expectancy ~ Adult.Mortality + infant.deaths + Measles +
## BMI + Total.expenditure + HIV.AIDS + GDP + Population + thinness..1.19.years +
## thinness.5.9.years + Income.composition.of.resources + Schooling +
## Developed + Developing + Hepatitis.B_below90 + Hepatitis.B_above90 +
## Polio_below90 + Polio_above90 + Diphtheria_below90
##
##
## Step: AIC=8166.65
## Life.expectancy ~ Adult.Mortality + infant.deaths + Measles +
## BMI + Total.expenditure + HIV.AIDS + GDP + Population + thinness..1.19.years +
## thinness.5.9.years + Income.composition.of.resources + Schooling +
## Developed + Developing + Hepatitis.B_below90 + Hepatitis.B_above90 +
## Polio_below90 + Diphtheria_below90
##
##
## Step: AIC=8166.65
## Life.expectancy ~ Adult.Mortality + infant.deaths + Measles +
## BMI + Total.expenditure + HIV.AIDS + GDP + Population + thinness..1.19.years +
## thinness.5.9.years + Income.composition.of.resources + Schooling +
## Developed + Developing + Hepatitis.B_below90 + Polio_below90 +
## Diphtheria_below90
##
##
## Step: AIC=8166.65
## Life.expectancy ~ Adult.Mortality + infant.deaths + Measles +
## BMI + Total.expenditure + HIV.AIDS + GDP + Population + thinness..1.19.years +
## thinness.5.9.years + Income.composition.of.resources + Schooling +
## Developed + Hepatitis.B_below90 + Polio_below90 + Diphtheria_below90
##
## Df Sum of Sq RSS AIC
## - infant.deaths 1 19.0 46816 8165.8
## - Hepatitis.B_below90 1 26.0 46823 8166.3
## - thinness.5.9.years 1 26.1 46823 8166.3
## <none> 46797 8166.7
## - Population 1 34.1 46831 8166.8
## - Total.expenditure 1 41.9 46839 8167.3
## - Measles 1 87.3 46884 8170.1
## - thinness..1.19.years 1 101.4 46898 8171.0
## - Developed 1 117.0 46914 8172.0
## - Diphtheria_below90 1 123.5 46921 8172.4
## - Polio_below90 1 260.8 47058 8181.0
## - GDP 1 808.5 47606 8215.0
## - BMI 1 908.0 47705 8221.1
## - Income.composition.of.resources 1 2332.9 49130 8307.6
## - Schooling 1 5721.7 52519 8503.6
## - Adult.Mortality 1 8154.5 54952 8636.6
## - HIV.AIDS 1 12211.4 59008 8845.9
##
## Step: AIC=8165.85
## Life.expectancy ~ Adult.Mortality + Measles + BMI + Total.expenditure +
## HIV.AIDS + GDP + Population + thinness..1.19.years + thinness.5.9.years +
## Income.composition.of.resources + Schooling + Developed +
## Hepatitis.B_below90 + Polio_below90 + Diphtheria_below90
##
## Df Sum of Sq RSS AIC
## - Population 1 18.4 46835 8165.0
## - thinness.5.9.years 1 21.7 46838 8165.2
## - Hepatitis.B_below90 1 25.4 46841 8165.4
## <none> 46816 8165.8
## - Total.expenditure 1 40.6 46857 8166.4
## - thinness..1.19.years 1 107.0 46923 8170.6
## - Developed 1 112.0 46928 8170.9
## - Diphtheria_below90 1 125.9 46942 8171.7
## - Measles 1 148.5 46965 8173.2
## - Polio_below90 1 264.2 47080 8180.4
## - GDP 1 808.8 47625 8214.2
## - BMI 1 900.2 47716 8219.8
## - Income.composition.of.resources 1 2317.7 49134 8305.8
## - Schooling 1 5748.3 52564 8504.1
## - Adult.Mortality 1 8147.9 54964 8635.3
## - HIV.AIDS 1 12197.0 59013 8844.1
##
## Step: AIC=8165.01
## Life.expectancy ~ Adult.Mortality + Measles + BMI + Total.expenditure +
## HIV.AIDS + GDP + thinness..1.19.years + thinness.5.9.years +
## Income.composition.of.resources + Schooling + Developed +
## Hepatitis.B_below90 + Polio_below90 + Diphtheria_below90
##
## Df Sum of Sq RSS AIC
## - thinness.5.9.years 1 23.6 46858 8164.5
## - Hepatitis.B_below90 1 26.2 46861 8164.6
## <none> 46835 8165.0
## - Total.expenditure 1 41.2 46876 8165.6
## - thinness..1.19.years 1 102.1 46937 8169.4
## - Developed 1 112.7 46947 8170.1
## - Diphtheria_below90 1 125.9 46960 8170.9
## - Measles 1 132.5 46967 8171.3
## - Polio_below90 1 262.3 47097 8179.4
## - GDP 1 807.1 47642 8213.2
## - BMI 1 914.3 47749 8219.8
## - Income.composition.of.resources 1 2341.1 49176 8306.3
## - Schooling 1 5771.0 52606 8504.4
## - Adult.Mortality 1 8153.1 54988 8634.5
## - HIV.AIDS 1 12267.7 59102 8846.5
##
## Step: AIC=8164.48
## Life.expectancy ~ Adult.Mortality + Measles + BMI + Total.expenditure +
## HIV.AIDS + GDP + thinness..1.19.years + Income.composition.of.resources +
## Schooling + Developed + Hepatitis.B_below90 + Polio_below90 +
## Diphtheria_below90
##
## Df Sum of Sq RSS AIC
## - Hepatitis.B_below90 1 25.5 46884 8164.1
## <none> 46858 8164.5
## - Total.expenditure 1 38.2 46896 8164.9
## - Developed 1 110.2 46968 8169.4
## - Diphtheria_below90 1 122.4 46980 8170.1
## - Measles 1 130.3 46988 8170.6
## - thinness..1.19.years 1 178.7 47037 8173.7
## - Polio_below90 1 261.8 47120 8178.9
## - GDP 1 800.3 47658 8212.2
## - BMI 1 893.0 47751 8217.9
## - Income.composition.of.resources 1 2351.6 49210 8306.3
## - Schooling 1 5799.4 52657 8505.3
## - Adult.Mortality 1 8137.6 54996 8632.9
## - HIV.AIDS 1 12261.7 59120 8845.4
##
## Step: AIC=8164.08
## Life.expectancy ~ Adult.Mortality + Measles + BMI + Total.expenditure +
## HIV.AIDS + GDP + thinness..1.19.years + Income.composition.of.resources +
## Schooling + Developed + Polio_below90 + Diphtheria_below90
##
## Df Sum of Sq RSS AIC
## <none> 46884 8164.1
## - Total.expenditure 1 40.5 46924 8164.6
## - Diphtheria_below90 1 97.8 46981 8168.2
## - Developed 1 122.5 47006 8169.7
## - Measles 1 127.4 47011 8170.1
## - thinness..1.19.years 1 181.1 47065 8173.4
## - Polio_below90 1 240.8 47124 8177.1
## - GDP 1 853.0 47737 8215.1
## - BMI 1 886.9 47771 8217.1
## - Income.composition.of.resources 1 2352.2 49236 8305.9
## - Schooling 1 5809.8 52693 8505.3
## - Adult.Mortality 1 8124.3 55008 8631.6
## - HIV.AIDS 1 12291.1 59175 8846.1summary(model_backward)##
## Call:
## lm(formula = Life.expectancy ~ Adult.Mortality + Measles + BMI +
## Total.expenditure + HIV.AIDS + GDP + thinness..1.19.years +
## Income.composition.of.resources + Schooling + Developed +
## Polio_below90 + Diphtheria_below90, data = life_exp1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -21.2357 -2.2519 -0.0019 2.3290 18.8733
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.821e+01 5.296e-01 109.932 < 2e-16 ***
## Adult.Mortality -1.782e-02 7.916e-04 -22.514 < 2e-16 ***
## Measles -1.885e-05 6.686e-06 -2.820 0.004839 **
## BMI 3.636e-02 4.888e-03 7.439 1.33e-13 ***
## Total.expenditure 5.161e-02 3.247e-02 1.590 0.112032
## HIV.AIDS -4.807e-01 1.736e-02 -27.692 < 2e-16 ***
## GDP 4.799e-05 6.579e-06 7.295 3.82e-13 ***
## thinness..1.19.years -7.126e-02 2.120e-02 -3.362 0.000785 ***
## Income.composition.of.resources 7.475e+00 6.171e-01 12.114 < 2e-16 ***
## Schooling 7.846e-01 4.121e-02 19.038 < 2e-16 ***
## Developed 6.870e-01 2.485e-01 2.765 0.005736 **
## Polio_below90 -1.431e+00 3.691e-01 -3.876 0.000108 ***
## Diphtheria_below90 -9.148e-01 3.703e-01 -2.470 0.013560 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.004 on 2925 degrees of freedom
## Multiple R-squared: 0.8237, Adjusted R-squared: 0.823
## F-statistic: 1139 on 12 and 2925 DF, p-value: < 2.2e-16Forward Direction
Model2 <- lm(Life.expectancy ~ 1, data = life_exp1)model_forward <- stepAIC(Model2, scope = list(lower = Model2, upper = Model1), direction = "forward")## Start: AIC=13239.02
## Life.expectancy ~ 1
##
## Df Sum of Sq RSS AIC
## + Schooling 1 154435 111481 10687
## + Income.composition.of.resources 1 144239 121678 10944
## + Adult.Mortality 1 129046 136870 11290
## + BMI 1 86804 179113 12080
## + Polio_below90 1 85316 180600 12104
## + Polio_above90 1 85316 180600 12104
## + Diphtheria_below90 1 85302 180615 12105
## + Diphtheria_above90 1 85302 180615 12105
## + HIV.AIDS 1 82413 183503 12151
## + Developed 1 61418 204499 12469
## + Developing 1 61418 204499 12469
## + thinness..1.19.years 1 61388 204529 12470
## + thinness.5.9.years 1 59840 206076 12492
## + GDP 1 53651 212265 12579
## + Hepatitis.B_below90 1 41593 224324 12741
## + Hepatitis.B_above90 1 41593 224324 12741
## + Total.expenditure 1 14122 251795 13081
## + infant.deaths 1 10313 255604 13125
## + Measles 1 6630 259287 13167
## + Population 1 289 265628 13238
## <none> 265917 13239
##
## Step: AIC=10686.94
## Life.expectancy ~ Schooling
##
## Df Sum of Sq RSS AIC
## + HIV.AIDS 1 41432 70049 9323.8
## + Adult.Mortality 1 38789 72692 9432.6
## + Income.composition.of.resources 1 10914 100567 10386.2
## + Polio_below90 1 10687 100794 10392.9
## + Polio_above90 1 10687 100794 10392.9
## + Diphtheria_below90 1 9905 101576 10415.6
## + Diphtheria_above90 1 9905 101576 10415.6
## + BMI 1 8050 103431 10468.7
## + Hepatitis.B_below90 1 4481 107000 10568.4
## + Hepatitis.B_above90 1 4481 107000 10568.4
## + thinness.5.9.years 1 4443 107038 10569.4
## + GDP 1 4367 107114 10571.5
## + thinness..1.19.years 1 4266 107215 10574.3
## + Developed 1 2346 109136 10626.5
## + Developing 1 2346 109136 10626.5
## + infant.deaths 1 338 111144 10680.0
## + Measles 1 279 111202 10681.6
## <none> 111481 10686.9
## + Total.expenditure 1 35 111446 10688.0
## + Population 1 1 111481 10688.9
##
## Step: AIC=9323.78
## Life.expectancy ~ Schooling + HIV.AIDS
##
## Df Sum of Sq RSS AIC
## + Adult.Mortality 1 12581.1 57468 8744.2
## + Income.composition.of.resources 1 6329.3 63720 9047.6
## + Polio_below90 1 4481.6 65568 9131.5
## + Polio_above90 1 4481.6 65568 9131.5
## + Diphtheria_below90 1 4231.3 65818 9142.7
## + Diphtheria_above90 1 4231.3 65818 9142.7
## + BMI 1 3738.7 66311 9164.6
## + GDP 1 3537.1 66512 9173.6
## + thinness.5.9.years 1 1911.6 68138 9244.5
## + thinness..1.19.years 1 1895.9 68153 9245.2
## + Hepatitis.B_below90 1 1709.7 68340 9253.2
## + Hepatitis.B_above90 1 1709.7 68340 9253.2
## + Developed 1 1692.6 68357 9253.9
## + Developing 1 1692.6 68357 9253.9
## + infant.deaths 1 541.3 69508 9303.0
## + Total.expenditure 1 358.9 69691 9310.7
## + Measles 1 326.7 69723 9312.1
## + Population 1 48.2 70001 9323.8
## <none> 70049 9323.8
##
## Step: AIC=8744.16
## Life.expectancy ~ Schooling + HIV.AIDS + Adult.Mortality
##
## Df Sum of Sq RSS AIC
## + Income.composition.of.resources 1 4225.0 53243 8521.8
## + Polio_below90 1 3338.7 54130 8570.3
## + Polio_above90 1 3338.7 54130 8570.3
## + Diphtheria_below90 1 3190.2 54278 8578.4
## + Diphtheria_above90 1 3190.2 54278 8578.4
## + BMI 1 2281.6 55187 8627.1
## + GDP 1 2256.1 55212 8628.5
## + thinness..1.19.years 1 1385.3 56083 8674.5
## + thinness.5.9.years 1 1304.3 56164 8678.7
## + Hepatitis.B_below90 1 1220.5 56248 8683.1
## + Hepatitis.B_above90 1 1220.5 56248 8683.1
## + Developed 1 1043.4 56425 8692.3
## + Developing 1 1043.4 56425 8692.3
## + infant.deaths 1 621.4 56847 8714.2
## + Measles 1 602.5 56866 8715.2
## + Total.expenditure 1 262.3 57206 8732.7
## + Population 1 67.1 57401 8742.7
## <none> 57468 8744.2
##
## Step: AIC=8521.81
## Life.expectancy ~ Schooling + HIV.AIDS + Adult.Mortality + Income.composition.of.resources
##
## Df Sum of Sq RSS AIC
## + Polio_below90 1 2783.03 50460 8366.1
## + Polio_above90 1 2783.03 50460 8366.1
## + Diphtheria_below90 1 2593.54 50650 8377.1
## + Diphtheria_above90 1 2593.54 50650 8377.1
## + BMI 1 1689.43 51554 8429.1
## + GDP 1 1421.53 51822 8444.3
## + thinness..1.19.years 1 1083.54 52160 8463.4
## + thinness.5.9.years 1 1033.44 52210 8466.2
## + Hepatitis.B_below90 1 1019.04 52224 8467.0
## + Hepatitis.B_above90 1 1019.04 52224 8467.0
## + infant.deaths 1 650.19 52593 8487.7
## + Developed 1 644.29 52599 8488.0
## + Developing 1 644.29 52599 8488.0
## + Measles 1 473.60 52770 8497.6
## + Total.expenditure 1 367.06 52876 8503.5
## + Population 1 87.46 53156 8519.0
## <none> 53243 8521.8
##
## Step: AIC=8366.08
## Life.expectancy ~ Schooling + HIV.AIDS + Adult.Mortality + Income.composition.of.resources +
## Polio_below90
##
## Df Sum of Sq RSS AIC
## + BMI 1 1591.39 48869 8273.9
## + GDP 1 1314.00 49146 8290.6
## + thinness..1.19.years 1 1086.74 49374 8304.1
## + thinness.5.9.years 1 954.28 49506 8312.0
## + Developed 1 586.01 49874 8333.8
## + Developing 1 586.01 49874 8333.8
## + infant.deaths 1 346.13 50114 8347.9
## + Total.expenditure 1 325.16 50135 8349.1
## + Measles 1 304.92 50155 8350.3
## + Diphtheria_below90 1 98.56 50362 8362.3
## + Diphtheria_above90 1 98.56 50362 8362.3
## + Hepatitis.B_below90 1 62.07 50398 8364.5
## + Hepatitis.B_above90 1 62.07 50398 8364.5
## <none> 50460 8366.1
## + Population 1 34.14 50426 8366.1
##
## Step: AIC=8273.93
## Life.expectancy ~ Schooling + HIV.AIDS + Adult.Mortality + Income.composition.of.resources +
## Polio_below90 + BMI
##
## Df Sum of Sq RSS AIC
## + GDP 1 1225.94 47643 8201.3
## + Developing 1 585.34 48284 8240.5
## + Developed 1 585.34 48284 8240.5
## + thinness..1.19.years 1 416.90 48452 8250.8
## + thinness.5.9.years 1 313.32 48556 8257.0
## + Measles 1 178.58 48690 8265.2
## + infant.deaths 1 171.23 48698 8265.6
## + Total.expenditure 1 166.56 48702 8265.9
## + Diphtheria_below90 1 116.41 48753 8268.9
## + Diphtheria_above90 1 116.41 48753 8268.9
## + Hepatitis.B_below90 1 62.77 48806 8272.2
## + Hepatitis.B_above90 1 62.77 48806 8272.2
## <none> 48869 8273.9
## + Population 1 10.86 48858 8275.3
##
## Step: AIC=8201.29
## Life.expectancy ~ Schooling + HIV.AIDS + Adult.Mortality + Income.composition.of.resources +
## Polio_below90 + BMI + GDP
##
## Df Sum of Sq RSS AIC
## + thinness..1.19.years 1 333.22 47310 8182.7
## + thinness.5.9.years 1 230.47 47413 8189.0
## + Developed 1 215.12 47428 8190.0
## + Developing 1 215.12 47428 8190.0
## + Measles 1 182.92 47460 8192.0
## + infant.deaths 1 161.07 47482 8193.3
## + Total.expenditure 1 148.67 47494 8194.1
## + Diphtheria_below90 1 112.31 47531 8196.4
## + Diphtheria_above90 1 112.31 47531 8196.4
## <none> 47643 8201.3
## + Population 1 7.35 47636 8202.8
## + Hepatitis.B_below90 1 6.34 47637 8202.9
## + Hepatitis.B_above90 1 6.34 47637 8202.9
##
## Step: AIC=8182.67
## Life.expectancy ~ Schooling + HIV.AIDS + Adult.Mortality + Income.composition.of.resources +
## Polio_below90 + BMI + GDP + thinness..1.19.years
##
## Df Sum of Sq RSS AIC
## + Developed 1 150.343 47159 8175.3
## + Developing 1 150.343 47159 8175.3
## + Measles 1 121.241 47189 8177.1
## + Diphtheria_below90 1 106.141 47204 8178.1
## + Diphtheria_above90 1 106.141 47204 8178.1
## + Total.expenditure 1 89.467 47220 8179.1
## <none> 47310 8182.7
## + infant.deaths 1 31.366 47278 8182.7
## + thinness.5.9.years 1 11.573 47298 8183.9
## + Population 1 4.207 47306 8184.4
## + Hepatitis.B_below90 1 4.175 47306 8184.4
## + Hepatitis.B_above90 1 4.175 47306 8184.4
##
## Step: AIC=8175.31
## Life.expectancy ~ Schooling + HIV.AIDS + Adult.Mortality + Income.composition.of.resources +
## Polio_below90 + BMI + GDP + thinness..1.19.years + Developed
##
## Df Sum of Sq RSS AIC
## + Measles 1 130.651 47029 8169.2
## + Diphtheria_below90 1 102.239 47057 8170.9
## + Diphtheria_above90 1 102.239 47057 8170.9
## + Total.expenditure 1 53.267 47106 8174.0
## + infant.deaths 1 41.453 47118 8174.7
## <none> 47159 8175.3
## + thinness.5.9.years 1 14.863 47145 8176.4
## + Population 1 3.368 47156 8177.1
## + Hepatitis.B_below90 1 0.730 47159 8177.3
## + Hepatitis.B_above90 1 0.730 47159 8177.3
##
## Step: AIC=8169.16
## Life.expectancy ~ Schooling + HIV.AIDS + Adult.Mortality + Income.composition.of.resources +
## Polio_below90 + BMI + GDP + thinness..1.19.years + Developed +
## Measles
##
## Df Sum of Sq RSS AIC
## + Diphtheria_below90 1 104.656 46924 8164.6
## + Diphtheria_above90 1 104.656 46924 8164.6
## + Total.expenditure 1 47.352 46981 8168.2
## <none> 47029 8169.2
## + Population 1 20.908 47008 8169.9
## + thinness.5.9.years 1 16.771 47012 8170.1
## + infant.deaths 1 1.871 47027 8171.0
## + Hepatitis.B_below90 1 1.145 47028 8171.1
## + Hepatitis.B_above90 1 1.145 47028 8171.1
##
## Step: AIC=8164.62
## Life.expectancy ~ Schooling + HIV.AIDS + Adult.Mortality + Income.composition.of.resources +
## Polio_below90 + BMI + GDP + thinness..1.19.years + Developed +
## Measles + Diphtheria_below90
##
## Df Sum of Sq RSS AIC
## + Total.expenditure 1 40.502 46884 8164.1
## <none> 46924 8164.6
## + Hepatitis.B_below90 1 27.810 46896 8164.9
## + Hepatitis.B_above90 1 27.810 46896 8164.9
## + Population 1 21.718 46902 8165.3
## + thinness.5.9.years 1 19.742 46904 8165.4
## + infant.deaths 1 1.029 46923 8166.6
##
## Step: AIC=8164.08
## Life.expectancy ~ Schooling + HIV.AIDS + Adult.Mortality + Income.composition.of.resources +
## Polio_below90 + BMI + GDP + thinness..1.19.years + Developed +
## Measles + Diphtheria_below90 + Total.expenditure
##
## Df Sum of Sq RSS AIC
## <none> 46884 8164.1
## + Hepatitis.B_below90 1 25.4928 46858 8164.5
## + Hepatitis.B_above90 1 25.4928 46858 8164.5
## + thinness.5.9.years 1 22.8700 46861 8164.6
## + Population 1 21.1256 46862 8164.8
## + infant.deaths 1 1.3254 46882 8166.0summary(model_forward)##
## Call:
## lm(formula = Life.expectancy ~ Schooling + HIV.AIDS + Adult.Mortality +
## Income.composition.of.resources + Polio_below90 + BMI + GDP +
## thinness..1.19.years + Developed + Measles + Diphtheria_below90 +
## Total.expenditure, data = life_exp1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -21.2357 -2.2519 -0.0019 2.3290 18.8733
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.821e+01 5.296e-01 109.932 < 2e-16 ***
## Schooling 7.846e-01 4.121e-02 19.038 < 2e-16 ***
## HIV.AIDS -4.807e-01 1.736e-02 -27.692 < 2e-16 ***
## Adult.Mortality -1.782e-02 7.916e-04 -22.514 < 2e-16 ***
## Income.composition.of.resources 7.475e+00 6.171e-01 12.114 < 2e-16 ***
## Polio_below90 -1.431e+00 3.691e-01 -3.876 0.000108 ***
## BMI 3.636e-02 4.888e-03 7.439 1.33e-13 ***
## GDP 4.799e-05 6.579e-06 7.295 3.82e-13 ***
## thinness..1.19.years -7.126e-02 2.120e-02 -3.362 0.000785 ***
## Developed 6.870e-01 2.485e-01 2.765 0.005736 **
## Measles -1.885e-05 6.686e-06 -2.820 0.004839 **
## Diphtheria_below90 -9.148e-01 3.703e-01 -2.470 0.013560 *
## Total.expenditure 5.161e-02 3.247e-02 1.590 0.112032
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.004 on 2925 degrees of freedom
## Multiple R-squared: 0.8237, Adjusted R-squared: 0.823
## F-statistic: 1139 on 12 and 2925 DF, p-value: < 2.2e-16Both Direction
model_both <- stepAIC(Model1, scope = list(lower = Model2, upper = Model1), direction = "both")## Start: AIC=8166.65
## Life.expectancy ~ Adult.Mortality + infant.deaths + Measles +
## BMI + Total.expenditure + HIV.AIDS + GDP + Population + thinness..1.19.years +
## thinness.5.9.years + Income.composition.of.resources + Schooling +
## Developed + Developing + Hepatitis.B_below90 + Hepatitis.B_above90 +
## Polio_below90 + Polio_above90 + Diphtheria_below90 + Diphtheria_above90
##
##
## Step: AIC=8166.65
## Life.expectancy ~ Adult.Mortality + infant.deaths + Measles +
## BMI + Total.expenditure + HIV.AIDS + GDP + Population + thinness..1.19.years +
## thinness.5.9.years + Income.composition.of.resources + Schooling +
## Developed + Developing + Hepatitis.B_below90 + Hepatitis.B_above90 +
## Polio_below90 + Polio_above90 + Diphtheria_below90
##
##
## Step: AIC=8166.65
## Life.expectancy ~ Adult.Mortality + infant.deaths + Measles +
## BMI + Total.expenditure + HIV.AIDS + GDP + Population + thinness..1.19.years +
## thinness.5.9.years + Income.composition.of.resources + Schooling +
## Developed + Developing + Hepatitis.B_below90 + Hepatitis.B_above90 +
## Polio_below90 + Diphtheria_below90
##
##
## Step: AIC=8166.65
## Life.expectancy ~ Adult.Mortality + infant.deaths + Measles +
## BMI + Total.expenditure + HIV.AIDS + GDP + Population + thinness..1.19.years +
## thinness.5.9.years + Income.composition.of.resources + Schooling +
## Developed + Developing + Hepatitis.B_below90 + Polio_below90 +
## Diphtheria_below90
##
##
## Step: AIC=8166.65
## Life.expectancy ~ Adult.Mortality + infant.deaths + Measles +
## BMI + Total.expenditure + HIV.AIDS + GDP + Population + thinness..1.19.years +
## thinness.5.9.years + Income.composition.of.resources + Schooling +
## Developed + Hepatitis.B_below90 + Polio_below90 + Diphtheria_below90
##
## Df Sum of Sq RSS AIC
## - infant.deaths 1 19.0 46816 8165.8
## - Hepatitis.B_below90 1 26.0 46823 8166.3
## - thinness.5.9.years 1 26.1 46823 8166.3
## <none> 46797 8166.7
## - Population 1 34.1 46831 8166.8
## - Total.expenditure 1 41.9 46839 8167.3
## - Measles 1 87.3 46884 8170.1
## - thinness..1.19.years 1 101.4 46898 8171.0
## - Developed 1 117.0 46914 8172.0
## - Diphtheria_below90 1 123.5 46921 8172.4
## - Polio_below90 1 260.8 47058 8181.0
## - GDP 1 808.5 47606 8215.0
## - BMI 1 908.0 47705 8221.1
## - Income.composition.of.resources 1 2332.9 49130 8307.6
## - Schooling 1 5721.7 52519 8503.6
## - Adult.Mortality 1 8154.5 54952 8636.6
## - HIV.AIDS 1 12211.4 59008 8845.9
##
## Step: AIC=8165.85
## Life.expectancy ~ Adult.Mortality + Measles + BMI + Total.expenditure +
## HIV.AIDS + GDP + Population + thinness..1.19.years + thinness.5.9.years +
## Income.composition.of.resources + Schooling + Developed +
## Hepatitis.B_below90 + Polio_below90 + Diphtheria_below90
##
## Df Sum of Sq RSS AIC
## - Population 1 18.4 46835 8165.0
## - thinness.5.9.years 1 21.7 46838 8165.2
## - Hepatitis.B_below90 1 25.4 46841 8165.4
## <none> 46816 8165.8
## - Total.expenditure 1 40.6 46857 8166.4
## + infant.deaths 1 19.0 46797 8166.7
## - thinness..1.19.years 1 107.0 46923 8170.6
## - Developed 1 112.0 46928 8170.9
## - Diphtheria_below90 1 125.9 46942 8171.7
## - Measles 1 148.5 46965 8173.2
## - Polio_below90 1 264.2 47080 8180.4
## - GDP 1 808.8 47625 8214.2
## - BMI 1 900.2 47716 8219.8
## - Income.composition.of.resources 1 2317.7 49134 8305.8
## - Schooling 1 5748.3 52564 8504.1
## - Adult.Mortality 1 8147.9 54964 8635.3
## - HIV.AIDS 1 12197.0 59013 8844.1
##
## Step: AIC=8165.01
## Life.expectancy ~ Adult.Mortality + Measles + BMI + Total.expenditure +
## HIV.AIDS + GDP + thinness..1.19.years + thinness.5.9.years +
## Income.composition.of.resources + Schooling + Developed +
## Hepatitis.B_below90 + Polio_below90 + Diphtheria_below90
##
## Df Sum of Sq RSS AIC
## - thinness.5.9.years 1 23.6 46858 8164.5
## - Hepatitis.B_below90 1 26.2 46861 8164.6
## <none> 46835 8165.0
## - Total.expenditure 1 41.2 46876 8165.6
## + Population 1 18.4 46816 8165.8
## + infant.deaths 1 3.4 46831 8166.8
## - thinness..1.19.years 1 102.1 46937 8169.4
## - Developed 1 112.7 46947 8170.1
## - Diphtheria_below90 1 125.9 46960 8170.9
## - Measles 1 132.5 46967 8171.3
## - Polio_below90 1 262.3 47097 8179.4
## - GDP 1 807.1 47642 8213.2
## - BMI 1 914.3 47749 8219.8
## - Income.composition.of.resources 1 2341.1 49176 8306.3
## - Schooling 1 5771.0 52606 8504.4
## - Adult.Mortality 1 8153.1 54988 8634.5
## - HIV.AIDS 1 12267.7 59102 8846.5
##
## Step: AIC=8164.48
## Life.expectancy ~ Adult.Mortality + Measles + BMI + Total.expenditure +
## HIV.AIDS + GDP + thinness..1.19.years + Income.composition.of.resources +
## Schooling + Developed + Hepatitis.B_below90 + Polio_below90 +
## Diphtheria_below90
##
## Df Sum of Sq RSS AIC
## - Hepatitis.B_below90 1 25.5 46884 8164.1
## <none> 46858 8164.5
## - Total.expenditure 1 38.2 46896 8164.9
## + thinness.5.9.years 1 23.6 46835 8165.0
## + Population 1 20.3 46838 8165.2
## + infant.deaths 1 1.6 46857 8166.4
## - Developed 1 110.2 46968 8169.4
## - Diphtheria_below90 1 122.4 46980 8170.1
## - Measles 1 130.3 46988 8170.6
## - thinness..1.19.years 1 178.7 47037 8173.7
## - Polio_below90 1 261.8 47120 8178.9
## - GDP 1 800.3 47658 8212.2
## - BMI 1 893.0 47751 8217.9
## - Income.composition.of.resources 1 2351.6 49210 8306.3
## - Schooling 1 5799.4 52657 8505.3
## - Adult.Mortality 1 8137.6 54996 8632.9
## - HIV.AIDS 1 12261.7 59120 8845.4
##
## Step: AIC=8164.08
## Life.expectancy ~ Adult.Mortality + Measles + BMI + Total.expenditure +
## HIV.AIDS + GDP + thinness..1.19.years + Income.composition.of.resources +
## Schooling + Developed + Polio_below90 + Diphtheria_below90
##
## Df Sum of Sq RSS AIC
## <none> 46884 8164.1
## + Hepatitis.B_below90 1 25.5 46858 8164.5
## + Hepatitis.B_above90 1 25.5 46858 8164.5
## - Total.expenditure 1 40.5 46924 8164.6
## + thinness.5.9.years 1 22.9 46861 8164.6
## + Population 1 21.1 46862 8164.8
## + infant.deaths 1 1.3 46882 8166.0
## - Diphtheria_below90 1 97.8 46981 8168.2
## - Developed 1 122.5 47006 8169.7
## - Measles 1 127.4 47011 8170.1
## - thinness..1.19.years 1 181.1 47065 8173.4
## - Polio_below90 1 240.8 47124 8177.1
## - GDP 1 853.0 47737 8215.1
## - BMI 1 886.9 47771 8217.1
## - Income.composition.of.resources 1 2352.2 49236 8305.9
## - Schooling 1 5809.8 52693 8505.3
## - Adult.Mortality 1 8124.3 55008 8631.6
## - HIV.AIDS 1 12291.1 59175 8846.1summary(model_both)##
## Call:
## lm(formula = Life.expectancy ~ Adult.Mortality + Measles + BMI +
## Total.expenditure + HIV.AIDS + GDP + thinness..1.19.years +
## Income.composition.of.resources + Schooling + Developed +
## Polio_below90 + Diphtheria_below90, data = life_exp1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -21.2357 -2.2519 -0.0019 2.3290 18.8733
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.821e+01 5.296e-01 109.932 < 2e-16 ***
## Adult.Mortality -1.782e-02 7.916e-04 -22.514 < 2e-16 ***
## Measles -1.885e-05 6.686e-06 -2.820 0.004839 **
## BMI 3.636e-02 4.888e-03 7.439 1.33e-13 ***
## Total.expenditure 5.161e-02 3.247e-02 1.590 0.112032
## HIV.AIDS -4.807e-01 1.736e-02 -27.692 < 2e-16 ***
## GDP 4.799e-05 6.579e-06 7.295 3.82e-13 ***
## thinness..1.19.years -7.126e-02 2.120e-02 -3.362 0.000785 ***
## Income.composition.of.resources 7.475e+00 6.171e-01 12.114 < 2e-16 ***
## Schooling 7.846e-01 4.121e-02 19.038 < 2e-16 ***
## Developed 6.870e-01 2.485e-01 2.765 0.005736 **
## Polio_below90 -1.431e+00 3.691e-01 -3.876 0.000108 ***
## Diphtheria_below90 -9.148e-01 3.703e-01 -2.470 0.013560 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.004 on 2925 degrees of freedom
## Multiple R-squared: 0.8237, Adjusted R-squared: 0.823
## F-statistic: 1139 on 12 and 2925 DF, p-value: < 2.2e-16All possible (Regsubsets)
library(leaps)
regs <- regsubsets(Life.expectancy ~., data = life_exp1, nbest=10)## Warning in leaps.setup(x, y, wt = wt, nbest = nbest, nvmax = nvmax, force.in =
## force.in, : 4 linear dependencies found## Reordering variables and trying again:plot(regs,
scale="adjr",
main="All possible regression: ranked by Adjusted R-squared")
The following variables, based on the supplied plot, are the most
important: Adult Mortality, BMI, GDP, HIV AIDS, thinness..1.19.years,
Income.composition.of.Resources, and Schooling. The significance of the
p-value for the specified variables was also reflected in other models
(three stars/***).
Model Construction Using Selected Variables
model_regs <- lm(formula = Life.expectancy ~ Adult.Mortality + BMI + GDP + HIV.AIDS + thinness..1.19.years + Income.composition.of.resources + Schooling, data = life_exp1)
summary(model_regs)##
## Call:
## lm(formula = Life.expectancy ~ Adult.Mortality + BMI + GDP +
## HIV.AIDS + thinness..1.19.years + Income.composition.of.resources +
## Schooling, data = life_exp1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -21.3454 -2.1298 -0.0851 2.2554 21.8040
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.545e+01 4.629e-01 119.805 < 2e-16 ***
## Adult.Mortality -1.843e-02 8.110e-04 -22.727 < 2e-16 ***
## BMI 3.805e-02 5.006e-03 7.600 3.96e-14 ***
## GDP 5.542e-05 6.493e-06 8.535 < 2e-16 ***
## HIV.AIDS -5.047e-01 1.770e-02 -28.512 < 2e-16 ***
## thinness..1.19.years -9.097e-02 2.124e-02 -4.284 1.90e-05 ***
## Income.composition.of.resources 8.178e+00 6.305e-01 12.972 < 2e-16 ***
## Schooling 9.373e-01 4.043e-02 23.184 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.127 on 2930 degrees of freedom
## Multiple R-squared: 0.8123, Adjusted R-squared: 0.8118
## F-statistic: 1811 on 7 and 2930 DF, p-value: < 2.2e-16Compare the Adj. R-Squared from All Models
data.frame(model = c("model_backward","model_forward","model_both", "model_regs"),
AdjRsquare = c(summary(model_backward)$adj.r.square,
summary(model_forward)$adj.r.square,
summary(model_both)$adj.r.square,
summary(model_regs)$adj.r.square))## model AdjRsquare
## 1 model_backward 0.8229672
## 2 model_forward 0.8229672
## 3 model_both 0.8229672
## 4 model_regs 0.8118388The model we will use to predict the ‘Life.expectancy’ will be model_backward, which we will select based on the supplied result.
Prediction
newData = data.frame(Adult.Mortality=55, Measles=4, BMI=23, Total.expenditure=1.23, HIV.AIDS = 23, GDP = 4235, thinness..1.19.years = 12, Income.composition.of.resources = 0.8, Schooling = 19, Developed = 0, Polio_below90 = 0, Diphtheria_below90 = 1)
predict(model_backward, newData)## 1
## 66.39876predict(model_backward, newData, interval="confidence", level = 0.99)## fit lwr upr
## 1 66.39876 64.7485 68.04902predicted=predict(model_backward, life_exp1)
predicted## 1 2 3 4 5 6 7 8
## 62.53524 62.26711 62.16433 61.90735 61.44841 61.17593 60.75759 60.41790
## 9 10 11 12 13 14 15 16
## 59.79887 59.47177 59.36032 58.35034 57.98504 62.59840 57.91175 57.52762
## 17 18 19 20 21 22 23 24
## 76.20788 77.37115 75.95013 75.82490 74.96086 73.94551 73.84116 75.01618
## 25 26 27 28 29 30 31 32
## 74.46019 70.94189 73.50867 73.60120 73.21808 73.26021 73.07832 73.12305
## 33 34 35 36 37 38 39 40
## 76.84333 76.90202 75.26686 75.12568 74.60659 74.06946 73.47527 72.70952
## 41 42 43 44 45 46 47 48
## 70.84526 72.29059 69.36420 71.32731 68.36805 68.22164 68.02480 67.80198
## 49 50 51 52 53 54 55 56
## 62.67439 61.78257 61.56393 60.57957 59.79209 58.63253 58.73899 58.26489
## 57 58 59 60 61 62 63 64
## 57.66446 57.00412 57.17968 56.70129 56.21848 55.59039 61.58557 61.07044
## 65 66 67 68 69 70 71 72
## 75.72930 74.91354 74.80593 74.68122 74.91998 74.87481 76.61278 74.45076
## 73 74 75 76 77 78 79 80
## 75.02599 75.01374 57.57648 55.71881 56.07674 57.29806 57.26066 57.19919
## 81 82 83 84 85 86 87 88
## 78.99514 78.82922 78.82007 80.62966 78.54490 77.68838 77.66873 77.46305
## 89 90 91 92 93 94 95 96
## 77.25752 77.01992 76.89438 79.04264 76.72813 76.76732 73.78286 73.58054
## 97 98 99 100 101 102 103 104
## 73.71721 75.68134 73.64809 73.62446 73.40452 72.95570 70.92440 72.28333
## 105 106 107 108 109 110 111 112
## 69.97095 69.25228 70.37677 71.28447 71.06114 70.97759 71.08924 71.11517
## 113 114 115 116 117 118 119 120
## 86.48200 87.57512 86.74027 86.53648 85.95242 85.17850 84.37249 84.62017
## 121 122 123 124 125 126 127 128
## 82.34892 84.82019 83.17514 81.46071 82.24857 82.62845 83.77267 80.45117
## 129 130 131 132 133 134 135 136
## 81.33991 81.80753 79.12155 82.46191 78.55990 78.47308 78.37476 77.84930
## 137 138 139 140 141 142 143 144
## 78.85891 75.12090 76.73171 76.41356 74.71749 78.38163 74.60178 74.43005
## 145 146 147 148 149 150 151 152
## 73.67048 73.62130 71.58070 72.10910 71.92615 72.37954 69.85783 69.77200
## 153 154 155 156 157 158 159 160
## 71.88268 68.44323 68.64389 68.49397 68.19152 67.93367 67.64084 69.78579
## 161 162 163 164 165 166 167 168
## 74.54986 76.46727 73.78245 74.15857 73.73845 73.80169 71.75403 71.42624
## 169 170 171 172 173 174 175 176
## 73.42342 73.35333 72.94236 73.03688 72.61853 75.49222 72.39311 66.32535
## 177 178 179 180 181 182 183 184
## 77.62952 78.85558 77.59169 77.50967 74.27751 74.33125 77.08383 76.17925
## 185 186 187 188 189 190 191 192
## 76.16830 75.87443 76.36237 76.11698 75.81362 74.97997 76.74089 75.13444
## 193 194 195 196 197 198 199 200
## 67.71985 67.42370 67.33406 67.13401 68.70534 66.03128 65.43963 65.44173
## 201 202 203 204 205 206 207 208
## 65.27457 64.95121 64.27718 64.18602 63.09961 62.79521 62.12925 61.76719
## 209 210 211 212 213 214 215 216
## 77.16286 78.88518 78.68463 76.22835 78.59669 74.10179 78.46929 73.54563
## 217 218 219 220 221 222 223 224
## 76.24802 73.58166 75.60563 75.25453 72.00829 72.05561 73.45453 72.68981
## 225 226 227 228 229 230 231 232
## 75.61369 75.68813 78.83244 73.26668 74.67746 74.50511 74.57422 74.24527
## 233 234 235 236 237 238 239 240
## 72.42351 73.12768 72.70687 72.40913 69.69105 71.54052 71.37708 71.25145
## 241 242 243 244 245 246 247 248
## 79.94802 81.53232 79.43854 79.30107 80.44355 78.90744 78.74574 81.22244
## 249 250 251 252 253 254 255 256
## 77.11156 78.64330 78.44050 82.86539 81.07864 81.02758 83.24702 81.86229
## 257 258 259 260 261 262 263 264
## 70.76349 70.75168 75.27054 71.87299 71.58038 71.73526 71.92659 71.94707
## 265 266 267 268 269 270 271 272
## 71.81601 71.25635 71.41873 71.01674 73.50723 69.77043 73.60502 69.02118
## 273 274 275 276 277 278 279 280
## 63.68413 63.47288 63.03403 62.67516 62.42736 62.05936 61.62574 60.93425
## 281 282 283 284 285 286 287 288
## 60.54367 60.34640 59.37800 58.99834 59.25930 58.83215 58.13934 58.00466
## 289 290 291 292 293 294 295 296
## 68.67593 68.43212 68.21340 67.90183 67.54452 62.12694 62.28517 61.98096
## 297 298 299 300 301 302 303 304
## 61.56178 60.95791 60.43300 57.48197 59.40416 56.73043 60.73882 57.85661
## 305 306 307 308 309 310 311 312
## 72.94357 72.82020 72.66072 70.92655 72.32770 73.99254 75.26251 69.70270
## 313 314 315 316 317 318 319 320
## 69.70185 69.64908 69.71349 69.74404 73.19371 69.08838 68.74774 68.16430
## 321 322 323 324 325 326 327 328
## 73.43800 73.44896 74.62784 73.97545 72.28066 72.40089 72.32233 74.17074
## 329 330 331 332 333 334 335 336
## 75.37966 74.49976 68.33391 65.80498 67.19871 66.96539 67.22116 55.72674
## 337 338 339 340 341 342 343 344
## 69.23326 68.94684 67.98234 72.14347 65.96313 64.95550 62.63612 59.99549
## 345 346 347 348 349 350 351 352
## 59.29333 57.47432 53.65952 48.12322 45.47941 43.30281 41.40884 41.95241
## 353 354 355 356 357 358 359 360
## 75.86418 75.40007 74.99455 74.89262 74.65765 74.24996 74.03441 71.87423
## 361 362 363 364 365 366 367 368
## 73.51120 73.34708 73.23640 76.09165 73.75479 73.57307 73.21450 72.93085
## 369 370 371 372 373 374 375 376
## 76.33977 76.32673 78.07563 77.80685 75.42001 76.94568 76.28913 76.83513
## 377 378 379 380 381 382 383 384
## 78.10061 74.84214 74.76280 74.37882 74.92517 74.56285 75.93672 75.16294
## 385 386 387 388 389 390 391 392
## 76.91438 74.58773 78.72751 76.32085 76.10801 75.32010 75.46989 75.38508
## 393 394 395 396 397 398 399 400
## 73.00809 72.81576 77.33277 74.56244 74.02528 73.91922 76.39690 73.61733
## 401 402 403 404 405 406 407 408
## 66.92343 62.51907 64.26087 59.37394 59.80268 59.31507 59.24422 59.43654
## 409 410 411 412 413 414 415 416
## 57.81792 62.70252 54.76583 52.71161 52.15238 51.05702 50.59361 50.22889
## 417 418 419 420 421 422 423 424
## 64.64857 64.46045 68.91370 63.61945 62.92205 67.20213 60.66628 63.75051
## 425 426 427 428 429 430 431 432
## 58.24793 55.85695 54.19474 53.26662 52.42892 52.04453 52.10241 51.76608
## 433 434 435 436 437 438 439 440
## 59.63626 66.14046 58.01697 59.53610 57.42722 58.18263 57.49144 57.27428
## 441 442 443 444 445 446 447 448
## 55.37505 55.29951 53.09141 54.77582 51.43814 50.28090 53.69246 53.10329
## 449 450 451 452 453 454 455 456
## 72.55781 71.48957 74.36196 71.82798 69.31326 71.36241 71.00054 70.75758
## 457 458 459 460 461 462 463 464
## 70.23870 70.00799 69.12060 71.20595 68.90973 68.81069 67.50052 61.99329
## 465 466 467 468 469 470 471 472
## 66.35086 66.12321 65.25677 65.02424 67.91971 64.53875 66.63710 66.39080
## 473 474 475 476 477 478 479 480
## 66.73954 62.98696 62.39027 61.56909 60.80547 59.55654 58.85203 58.30906
## 481 482 483 484 485 486 487 488
## 60.92966 60.40917 60.23432 59.79064 59.17756 64.59995 57.71742 56.99515
## 489 490 491 492 493 494 495 496
## 55.81637 55.85586 62.79646 55.32852 55.13636 61.77281 60.23915 53.31214
## 497 498 499 500 501 502 503 504
## 81.65569 78.77230 81.19940 81.15948 76.48336 80.03223 77.72248 79.07597
## 505 506 507 508 509 510 511 512
## 79.37638 78.81541 80.25553 78.00873 76.32444 77.09182 78.25334 76.96047
## 513 514 515 516 517 518 519 520
## 55.52328 54.50360 54.09848 54.25904 52.89461 52.21921 52.16508 51.13457
## 521 522 523 524 525 526 527 528
## 50.31898 57.40109 48.59126 47.95208 56.35227 55.73487 55.40393 55.19733
## 529 530 531 532 533 534 535 536
## 57.14992 56.89553 56.73111 56.38264 55.54103 55.50279 60.69656 53.91465
## 537 538 539 540 541 542 543 544
## 53.93446 53.27362 59.88893 59.76166 59.41331 58.99225 59.18109 56.51258
## 545 546 547 548 549 550 551 552
## 79.15416 79.03483 77.05941 75.96394 77.44647 75.20280 77.21081 77.06617
## 553 554 555 556 557 558 559 560
## 78.04703 77.00799 76.60329 75.88429 77.50340 77.10903 76.79312 76.41055
## 561 562 563 564 565 566 567 568
## 73.18990 72.87582 71.57202 71.85462 72.93894 71.77703 71.35285 69.36613
## 569 570 571 572 573 574 575 576
## 69.22263 68.81272 65.61534 67.68592 67.31618 67.23831 66.51250 64.19678
## 577 578 579 580 581 582 583 584
## 74.01847 71.98883 73.59797 73.87138 71.21955 72.98456 75.19558 72.60063
## 585 586 587 588 589 590 591 592
## 72.25647 71.60556 69.71976 68.89808 73.94354 68.82017 68.67765 68.50603
## 593 594 595 596 597 598 599 600
## 66.99429 68.26519 64.28204 64.08726 64.03460 63.85008 63.39374 62.60985
## 601 602 603 604 605 606 607 608
## 62.29637 62.74131 62.33460 58.86371 58.55158 59.62815 57.89333 57.67509
## 609 610 611 612 613 614 615 616
## 63.57089 63.31488 63.28335 62.15987 62.15925 61.53156 60.93347 59.98824
## 617 618 619 620 621 622 623 624
## 59.07178 58.31506 57.38389 63.14025 55.76006 55.46198 56.17195 56.16314
## 625 626 627 628 629 630 631 632
## 72.16426 74.02143 75.70432 75.47074 74.27878 73.07850 75.78243 72.34805
## 633 634 635 636 637 638 639 640
## 72.31713 71.92444 73.23788 72.24639 72.81169 72.87703 73.07127 74.70941
## 641 642 643 644 645 646 647 648
## 70.28922 78.52182 78.33822 78.14377 79.33295 79.23558 76.32878 76.85722
## 649 650 651 652 653 654 655 656
## 77.18400 77.00964 76.48698 75.64176 75.74096 74.79596 74.44044 74.34325
## 657 658 659 660 661 662 663 664
## 74.15706 75.73560 73.86782 76.22492 77.25141 77.29949 78.27883 80.40104
## 665 666 667 668 669 670 671 672
## 79.28403 78.20090 76.37052 75.80892 74.59345 74.36387 74.90325 71.29483
## 673 674 675 676 677 678 679 680
## 72.70337 76.17672 77.86891 77.68022 78.88049 78.98843 78.22704 78.71140
## 681 682 683 684 685 686 687 688
## 77.33324 78.39685 78.01634 77.95242 77.76916 76.34219 76.46036 75.58025
## 689 690 691 692 693 694 695 696
## 77.35914 79.70133 79.25400 81.72096 78.82313 77.85041 78.97222 80.45046
## 697 698 699 700 701 702 703 704
## 79.78945 79.08310 79.32343 77.37756 73.57404 73.08492 79.46348 76.13492
## 705 706 707 708 709 710 711 712
## 75.59429 71.68432 71.14399 70.79531 69.28203 68.53047 68.40481 65.05712
## 713 714 715 716 717 718 719 720
## 63.65669 68.93664 69.35268 69.51000 62.12093 66.54114 66.78592 66.72872
## 721 722 723 724 725 726 727 728
## 64.59937 60.37143 60.09171 56.61620 53.55242 57.80683 58.42780 58.97923
## 729 730 731 732 733 734 735 736
## 56.89766 53.07332 55.83168 51.28344 53.96944 50.81960 52.98849 53.80545
## 737 738 739 740 741 742 743 744
## 48.09027 82.29626 84.67202 84.64690 81.23050 82.57495 77.84797 80.29177
## 745 746 747 748 749 750 751 752
## 80.00961 79.98029 79.88949 81.70391 81.35187 80.61853 82.09712 80.27032
## 753 754 755 756 757 758 759 760
## 80.44783 60.31090 59.74384 60.08795 59.98082 59.04113 58.41722 58.01413
## 761 762 763 764 765 766 767 768
## 57.47371 55.68563 59.94693 54.49290 54.98520 54.62419 54.36484 53.93905
## 769 770 771 772 773 774 775 776
## 53.97994 74.65149 71.22406 71.97109 70.65629 70.43158 72.95010 70.02235
## 777 778 779 780 781 782 783 784
## 69.94634 69.41405 67.66307 68.72945 71.18765 67.62853 70.89027 67.60814
## 785 786 787 788 789 790 791 792
## 67.62757 67.57878 72.46842 72.79928 71.83345 71.51472 71.47803 70.52343
## 793 794 795 796 797 798 799 800
## 71.83207 73.30397 75.18413 72.68769 71.06914 70.06793 71.32971 69.65626
## 801 802 803 804 805 806 807 808
## 69.35162 69.25773 73.43724 71.11666 72.91326 72.41702 72.17087 71.82017
## 809 810 811 812 813 814 815 816
## 71.55144 71.42077 71.18442 70.84083 70.78732 70.48569 70.50993 70.37946
## 817 818 819 820 821 822 823 824
## 70.19542 68.48971 72.95688 72.74386 72.66229 72.59233 69.74351 69.71284
## 825 826 827 828 829 830 831 832
## 74.93917 72.13106 73.11773 69.76504 68.92327 68.51126 73.77232 71.13540
## 833 834 835 836 837 838 839 840
## 69.88365 69.56725 65.36530 65.22466 59.43628 58.93292 58.97801 59.17071
## 841 842 843 844 845 846 847 848
## 63.79017 59.69652 58.74183 58.75104 58.01712 59.37369 59.82813 59.86146
## 849 850 851 852 853 854 855 856
## 59.76958 49.66155 60.80671 60.62411 60.44475 60.19947 59.91761 57.28423
## 857 858 859 860 861 862 863 864
## 59.36975 59.16914 58.97542 58.77914 61.07826 55.16341 54.85344 53.70620
## 865 866 867 868 869 870 871 872
## 52.73770 48.03555 77.93002 78.67742 77.68457 78.21624 77.95061 77.64625
## 873 874 875 876 877 878 879 880
## 77.26561 76.41470 76.59400 76.34270 75.54405 75.18454 75.26254 74.49881
## 881 882 883 884 885 886 887 888
## 74.03330 73.35058 61.94753 61.81040 61.66348 61.45594 61.00468 59.82729
## 889 890 891 892 893 894 895 896
## 59.30664 58.26763 62.05325 56.11884 54.85810 54.03859 53.54657 52.97607
## 897 898 899 900 901 902 903 904
## 52.16670 49.35647 74.79256 77.41177 74.27343 72.09226 73.81387 77.10628
## 905 906 907 908 909 910 911 912
## 76.60115 76.34429 75.99042 72.70176 72.55697 71.97742 75.29829 75.22604
## 913 914 915 916 917 918 919 920
## 71.42589 68.77760 79.73187 81.84177 81.77063 81.56063 77.12934 77.16805
## 921 922 923 924 925 926 927 928
## 79.25737 79.23890 81.33435 79.14297 82.19915 83.06668 81.10212 80.67843
## 929 930 931 932 933 934 935 936
## 81.98939 81.29448 80.80087 80.98556 80.89463 78.93627 76.62264 76.44253
## 937 938 939 940 941 942 943 944
## 80.39777 80.14117 77.92022 79.56048 78.90278 78.70933 78.36049 79.60228
## 945 946 947 948 949 950 951 952
## 80.06964 79.89122 67.03684 66.82986 65.92737 64.84300 63.63265 63.35676
## 953 954 955 956 957 958 959 960
## 67.00992 61.70931 61.64325 60.96867 64.57417 59.26206 65.39426 60.21358
## 961 962 963 964 965 966 967 968
## 65.48546 61.15917 63.94205 63.85791 63.78649 63.65188 63.21784 62.94930
## 969 970 971 972 973 974 975 976
## 62.61247 62.15132 61.82559 61.56814 60.46429 57.85799 58.21351 58.00380
## 977 978 979 980 981 982 983 984
## 63.76225 63.01504 74.92351 74.55832 74.33770 76.45150 72.85035 72.25983
## 985 986 987 988 989 990 991 992
## 72.16542 70.85694 73.88879 70.91176 70.36019 69.90250 69.83892 69.59525
## 993 994 995 996 997 998 999 1000
## 69.79029 64.30840 82.52566 80.81623 80.63755 78.18132 77.98142 82.05265
## 1001 1002 1003 1004 1005 1006 1007 1008
## 81.98625 82.79978 81.23479 80.77554 80.55899 80.44983 80.21010 78.56155
## 1009 1010 1011 1012 1013 1014 1015 1016
## 79.37171 78.46042 65.23752 67.61889 66.46665 66.98632 66.37495 65.61746
## 1017 1018 1019 1020 1021 1022 1023 1024
## 65.24602 64.56017 68.06908 60.53009 59.67497 63.85432 63.71162 62.64738
## 1025 1026 1027 1028 1029 1030 1031 1032
## 62.77167 62.87689 79.72265 80.64119 80.54149 80.25398 80.37161 80.12251
## 1033 1034 1035 1036 1037 1038 1039 1040
## 78.77669 79.89679 81.34165 78.70635 76.97659 78.53465 78.22753 76.83181
## 1041 1042 1043 1044 1045 1046 1047 1048
## 75.46880 73.63889 75.95160 74.36145 75.69241 75.60206 77.55261 69.82812
## 1049 1050 1051 1052 1053 1054 1055 1056
## 69.56351 69.31153 69.14472 68.88780 67.33860 65.81639 68.26693 68.04476
## 1057 1058 1059 1060 1061 1062 1063 1064
## 67.72430 67.63726 66.06522 67.55500 67.46900 69.74226 67.16120 69.36961
## 1065 1066 1067 1068 1069 1070 1071 1072
## 69.18384 72.30007 66.52460 69.22296 68.80495 68.72197 68.37773 68.15277
## 1073 1074 1075 1076 1077 1078 1079 1080
## 64.52684 62.69363 61.16652 60.73317 60.57459 59.96626 64.32613 58.75077
## 1081 1082 1083 1084 1085 1086 1087 1088
## 58.33618 63.43908 63.02738 57.42350 56.66372 55.16342 55.69245 55.28853
## 1089 1090 1091 1092 1093 1094 1095 1096
## 55.44761 55.18823 60.57284 60.28946 59.67025 59.13755 58.72593 58.56990
## 1097 1098 1099 1100 1101 1102 1103 1104
## 58.43709 58.12541 62.90094 61.73513 58.62698 59.10417 59.06338 59.13063
## 1105 1106 1107 1108 1109 1110 1111 1112
## 59.68287 60.16327 68.84849 68.58889 68.69536 72.42967 68.37492 68.20536
## 1113 1114 1115 1116 1117 1118 1119 1120
## 68.66503 67.24759 66.78356 72.45555 68.00174 67.73309 66.65971 67.17819
## 1121 1122 1123 1124 1125 1126 1127 1128
## 64.97995 65.23339 67.95345 63.93344 63.74875 63.37699 62.31017 54.87582
## 1129 1130 1131 1132 1133 1134 1135 1136
## 62.23528 61.70240 60.03309 65.12749 64.62634 64.30193 64.59799 63.83727
## 1137 1138 1139 1140 1141 1142 1143 1144
## 63.58959 63.43364 71.11725 69.57612 73.65667 71.23477 71.06928 70.86168
## 1145 1146 1147 1148 1149 1150 1151 1152
## 70.59822 70.25788 72.47883 69.66597 69.35116 68.93295 68.69181 66.99743
## 1153 1154 1155 1156 1157 1158 1159 1160
## 67.93730 66.23613 78.14249 78.31554 77.85199 77.67137 79.42787 76.76884
## 1161 1162 1163 1164 1165 1166 1167 1168
## 77.17582 75.21828 76.86321 76.59880 76.28017 78.94596 75.90763 75.15964
## 1169 1170 1171 1172 1173 1174 1175 1176
## 74.73939 74.49855 82.64869 80.52578 81.28665 82.50083 81.76144 83.56310
## 1177 1178 1179 1180 1181 1182 1183 1184
## 81.74033 83.93698 84.48130 81.33029 83.54305 83.30861 80.21575 82.63242
## 1185 1186 1187 1188 1189 1190 1191 1192
## 81.13453 80.95253 63.58529 63.69838 64.71021 67.35584 63.48156 63.03962
## 1193 1194 1195 1196 1197 1198 1199 1200
## 65.98761 65.52893 65.15116 64.46466 61.35683 60.73830 60.26976 60.12835
## 1201 1202 1203 1204 1205 1206 1207 1208
## 59.72036 59.84982 68.83134 68.68852 68.51490 68.17611 67.67981 67.44324
## 1209 1210 1211 1212 1213 1214 1215 1216
## 66.90201 66.89498 68.67882 66.12281 69.29987 65.47391 65.68693 65.02483
## 1217 1218 1219 1220 1221 1222 1223 1224
## 65.17906 65.14743 76.26077 76.17475 76.24410 74.97108 74.21876 75.48305
## 1225 1226 1227 1228 1229 1230 1231 1232
## 73.32815 72.30997 70.24289 71.43405 71.38182 71.63764 70.99104 71.30282
## 1233 1234 1235 1236 1237 1238 1239 1240
## 70.89961 73.07664 67.54897 67.16056 70.87479 68.63582 68.39470 68.08656
## 1241 1242 1243 1244 1245 1246 1247 1248
## 67.54113 67.60847 66.44039 65.91161 69.73197 69.33079 65.72352 67.43105
## 1249 1250 1251 1252 1253 1254 1255 1256
## 64.62366 66.19133 81.96396 81.97707 81.87124 81.83394 85.12598 83.59462
## 1257 1258 1259 1260 1261 1262 1263 1264
## 83.39871 83.79787 83.44054 82.95576 78.13161 79.65631 77.23229 78.14166
## 1265 1266 1267 1268 1269 1270 1271 1272
## 77.76257 77.31778 80.79582 81.77335 80.61651 81.37236 80.29165 78.72107
## 1273 1274 1275 1276 1277 1278 1279 1280
## 79.74122 79.92408 78.33515 78.40546 76.44199 77.33784 79.28537 77.67373
## 1281 1282 1283 1284 1285 1286 1287 1288
## 77.50869 77.56644 80.01725 81.61003 80.20003 82.69154 82.55313 82.49181
## 1289 1290 1291 1292 1293 1294 1295 1296
## 79.49795 79.62173 81.17133 79.35702 80.49657 80.22270 79.50564 79.07363
## 1297 1298 1299 1300 1301 1302 1303 1304
## 77.80622 76.68760 73.75677 73.40800 71.64459 73.05686 72.91584 71.43878
## 1305 1306 1307 1308 1309 1310 1311 1312
## 70.54802 72.63625 72.17624 74.33920 71.25234 69.96960 70.55946 70.33312
## 1313 1314 1315 1316 1317 1318 1319 1320
## 69.58624 69.83824 79.29186 77.70127 77.69939 77.63447 79.42046 77.70917
## 1321 1322 1323 1324 1325 1326 1327 1328
## 77.60894 78.96195 78.89808 78.75557 78.79203 78.54347 77.94555 77.28889
## 1329 1330 1331 1332 1333 1334 1335 1336
## 76.28947 76.87232 74.48663 74.42493 74.53399 74.18415 74.33639 74.54605
## 1337 1338 1339 1340 1341 1342 1343 1344
## 72.92064 72.80693 76.57304 74.66713 74.47973 74.23253 73.95023 73.71595
## 1345 1346 1347 1348 1349 1350 1351 1352
## 73.37404 73.17027 74.36561 77.45257 77.26712 72.52097 73.64254 72.89861
## 1353 1354 1355 1356 1357 1358 1359 1360
## 73.25636 72.85709 72.24197 71.68793 70.97427 69.93599 70.42875 70.15408
## 1361 1362 1363 1364 1365 1366 1367 1368
## 69.48997 69.18250 63.41793 65.63791 63.89101 64.64626 64.70077 61.53351
## 1369 1370 1371 1372 1373 1374 1375 1376
## 60.33504 58.97394 57.05741 55.45065 54.25660 52.45537 51.09462 50.72843
## 1377 1378 1379 1380 1381 1382 1383 1384
## 49.86350 49.19628 69.11118 72.52428 74.43792 74.33754 74.31278 74.26489
## 1385 1386 1387 1388 1389 1390 1391 1392
## 72.36371 72.20293 71.38004 68.62985 64.34520 64.39516 61.87318 65.59364
## 1393 1394 1395 1396 1397 1398 1399 1400
## 63.06497 62.62252 77.03090 75.06707 75.38901 77.83874 77.81051 77.37303
## 1401 1402 1403 1404 1405 1406 1407 1408
## 77.41342 78.29445 77.88872 77.88963 77.52094 77.35798 75.89168 76.43810
## 1409 1410 1411 1412 1413 1414 1415 1416
## 75.71628 76.50497 71.76450 74.52541 71.51023 73.97614 70.63689 67.77306
## 1417 1418 1419 1420 1421 1422 1423 1424
## 72.54321 70.35712 70.12939 69.95399 69.97542 70.05386 69.75013 69.73467
## 1425 1426 1427 1428 1429 1430 1431 1432
## 69.34548 68.79760 65.45782 64.42776 67.27610 67.56655 63.90039 63.54985
## 1433 1434 1435 1436 1437 1438 1439 1440
## 63.28876 62.86902 62.54967 66.25129 62.61233 62.32447 61.94666 61.46152
## 1441 1442 1443 1444 1445 1446 1447 1448
## 61.32826 61.09846 77.93376 75.91568 74.58655 77.16562 76.67690 80.04494
## 1449 1450 1451 1452 1453 1454 1455 1456
## 77.48145 77.29346 76.07291 76.24617 75.97788 78.87274 78.37677 74.50587
## 1457 1458 1459 1460 1461 1462 1463 1464
## 73.68909 73.35510 72.69232 72.95062 72.62074 73.08416 72.96508 72.96762
## 1465 1466 1467 1468 1469 1470 1471 1472
## 72.40344 72.30467 72.05768 74.23223 66.96505 67.33686 69.72452 69.58809
## 1473 1474 1475 1476 1477 1478 1479 1480
## 69.52516 67.62323 56.80440 55.99679 56.62329 57.27237 64.67891 55.07489
## 1481 1482 1483 1484 1485 1486 1487 1488
## 50.87852 44.91128 42.68486 40.28298 39.47361 39.72797 40.84627 41.84215
## 1489 1490 1491 1492 1493 1494 1495 1496
## 42.35921 43.17951 62.44135 61.11215 62.52716 61.79521 61.88462 61.65138
## 1497 1498 1499 1500 1501 1502 1503 1504
## 61.59899 61.26568 60.39141 64.86429 60.10247 59.61041 64.78037 58.49497
## 1505 1506 1507 1508 1509 1510 1511 1512
## 59.32712 62.66196 73.84287 73.76372 73.96276 73.99948 72.05776 74.69533
## 1513 1514 1515 1516 1517 1518 1519 1520
## 74.89322 75.62367 75.19710 75.73022 75.78745 75.48594 75.73340 75.20780
## 1521 1522 1523 1524 1525 1526 1527 1528
## 75.40563 75.15714 78.25034 78.27189 77.91661 75.95804 78.89668 75.84517
## 1529 1530 1531 1532 1533 1534 1535 1536
## 77.55098 76.94564 80.21276 75.95713 76.16068 77.92088 78.92227 78.60455
## 1537 1538 1539 1540 1541 1542 1543 1544
## 77.85606 77.68914 77.94708 81.52596 81.21318 77.63445 83.19642 78.11262
## 1545 1546 1547 1548 1549 1550 1551 1552
## 77.85501 83.85684 77.00976 81.24218 78.62794 80.32349 79.84491 76.79794
## 1553 1554 1555 1556 1557 1558 1559 1560
## 78.64828 78.65526 67.05455 63.35798 67.57063 63.63743 63.53107 63.35542
## 1561 1562 1563 1564 1565 1566 1567 1568
## 62.80403 62.35893 61.99905 61.82847 61.66070 60.70118 59.88583 60.67960
## 1569 1570 1571 1572 1573 1574 1575 1576
## 60.46721 56.34584 59.85591 60.33146 57.98286 66.13201 57.41080 51.19882
## 1577 1578 1579 1580 1581 1582 1583 1584
## 53.37170 51.47793 47.71008 48.50833 57.12669 46.09834 44.43615 54.09995
## 1585 1586 1587 1588 1589 1590 1591 1592
## 44.20510 44.74047 72.43191 73.61630 72.97732 72.84831 74.84831 72.53615
## 1593 1594 1595 1596 1597 1598 1599 1600
## 72.58205 72.39563 72.03806 72.21296 71.27356 71.90450 71.40346 73.44200
## 1601 1602 1603 1604 1605 1606 1607 1608
## 70.96891 70.28446 73.16191 73.26866 72.71415 72.22707 71.76656 71.09378
## 1609 1610 1611 1612 1613 1614 1615 1616
## 71.22495 70.60420 70.80102 70.91586 70.93549 72.14957 69.95595 69.66552
## 1617 1618 1619 1620 1621 1622 1623 1624
## 69.34914 68.88376 60.90746 60.56944 60.23663 64.35021 59.77151 58.74074
## 1625 1626 1627 1628 1629 1630 1631 1632
## 58.40014 57.82368 58.17058 57.61639 61.81532 57.33710 56.80261 61.17977
## 1633 1634 1635 1636 1637 1638 1639 1640
## 60.64342 59.72677 79.82402 78.51259 78.23831 78.06869 79.59475 75.91460
## 1641 1642 1643 1644 1645 1646 1647 1648
## 75.71673 76.74452 76.40252 76.58748 78.81814 75.18209 77.69538 77.44917
## 1649 1650 1651 1652 1653 1654 1655 1656
## 76.70200 77.97695 62.77687 65.20438 65.24762 65.70507 65.25960 61.82261
## 1657 1658 1659 1660 1661 1662 1663 1664
## 61.58665 61.12641 61.09293 61.14340 60.86650 60.79522 60.81782 60.66750
## 1665 1666 1667 1668 1669 1670 1671 1672
## 62.05733 60.51792 64.18962 74.72026 73.80828 74.18566 73.63481 73.34679
## 1673 1674 1675 1676 1677 1678 1679 1680
## 71.62409 71.72586 72.11434 72.32916 72.06703 71.58028 71.33402 70.92351
## 1681 1682 1683 1684 1685 1686 1687 1688
## 68.34961 70.36475 67.86922 72.74342 72.12545 73.88864 74.02015 72.34699
## 1689 1690 1691 1692 1693 1694 1695 1696
## 72.10232 76.01015 73.86692 73.42389 73.58833 73.50376 73.34428 73.03638
## 1697 1698 1699 1700 1701 1702 1703 1704
## 72.41064 72.36518 72.05133 69.98172 70.12653 70.00448 69.92680 69.91237
## 1705 1706 1707 1708 1709 1710 1711 1712
## 69.71122 70.46716 69.30521 69.03741 68.87430 71.03326 67.92361 71.93616
## 1713 1714 1715 1716 1717 1718 1719 1720
## 70.68383 67.75620 55.16414 75.70449 73.13006 73.37868 71.50394 72.96525
## 1721 1722 1723 1724 1725 1726 1727 1728
## 72.67275 75.92463 71.80136 71.56698 74.65067 69.86453 69.02275 68.22011
## 1729 1730 1731 1732 1733 1734 1735 1736
## 66.46984 67.46235 66.54547 66.09093 76.20449 78.49953 76.43989 76.55574
## 1737 1738 1739 1740 1741 1742 1743 1744
## 76.66401 76.45201 76.05635 75.55710 74.86936 74.08579 72.45915 73.48430
## 1745 1746 1747 1748 1749 1750 1751 1752
## 55.82672 57.95068 57.91563 57.75840 72.90513 72.82432 72.72324 72.04864
## 1753 1754 1755 1756 1757 1758 1759 1760
## 73.12265 72.79978 70.66718 70.27283 68.18943 69.65106 69.28892 68.89339
## 1761 1762 1763 1764 1765 1766 1767 1768
## 68.37905 70.28960 67.46147 69.33020 58.78253 58.35308 63.60864 62.73558
## 1769 1770 1771 1772 1773 1774 1775 1776
## 61.02330 60.13325 60.55376 59.40411 51.35922 49.90394 49.15362 49.07899
## 1777 1778 1779 1780 1781 1782 1783 1784
## 48.74940 49.22939 55.84288 56.14338 63.53608 66.66875 66.49400 66.28519
## 1785 1786 1787 1788 1789 1790 1791 1792
## 65.49868 65.79543 62.17636 60.27047 61.45420 64.77791 61.06715 62.22768
## 1793 1794 1795 1796 1797 1798 1799 1800
## 60.58140 60.40864 60.18939 59.98295 67.95256 65.77105 65.58885 64.83933
## 1801 1802 1803 1804 1805 1806 1807 1808
## 63.36196 62.67327 66.01292 57.55086 55.99926 52.86753 50.69995 49.58756
## 1809 1810 1811 1812 1813 1814 1815 1816
## 49.32552 49.67039 50.35325 57.47097 70.33218 67.29795 69.01703 68.80275
## 1817 1818 1819 1820 1821 1822 1823 1824
## 66.21328 68.19745 64.92236 65.63664 63.67113 63.40419 67.46085 65.62196
## 1825 1826 1827 1828 1829 1830 1831 1832
## 61.95096 65.29314 60.99602 65.01904 61.05443 83.70997 83.68764 85.00037
## 1833 1834 1835 1836 1837 1838 1839 1840
## 81.94633 80.47733 80.24071 79.87791 82.84582 82.34032 81.80889 81.52405
## 1841 1842 1843 1844 1845 1846 1847 1848
## 81.32814 82.26270 80.93930 80.57007 80.24093 82.77704 82.72161 84.58149
## 1849 1850 1851 1852 1853 1854 1855 1856
## 83.94614 84.52782 84.76437 82.29035 81.04128 79.74146 79.60593 79.36479
## 1857 1858 1859 1860 1861 1862 1863 1864
## 78.88789 77.58946 76.70912 78.37101 78.07018 71.86798 71.77059 71.40159
## 1865 1866 1867 1868 1869 1870 1871 1872
## 71.33458 69.70102 69.42269 70.74493 70.41802 70.17886 70.41786 67.23972
## 1873 1874 1875 1876 1877 1878 1879 1880
## 67.12359 66.98915 66.61994 66.36121 66.06380 62.25878 58.66182 59.14555
## 1881 1882 1883 1884 1885 1886 1887 1888
## 58.76839 58.30225 57.65441 56.43583 55.90588 55.58926 55.38958 55.01107
## 1889 1890 1891 1892 1893 1894 1895 1896
## 53.42523 57.90795 53.68127 53.05907 53.67798 60.05219 60.31809 59.10012
## 1897 1898 1899 1900 1901 1902 1903 1904
## 59.40369 58.19823 58.16072 57.90603 57.39400 56.60705 56.81607 61.55346
## 1905 1906 1907 1908 1909 1910 1911 1912
## 61.83455 56.19488 57.50883 55.47835 54.43451 75.55101 82.00653 79.45623
## 1913 1914 1915 1916 1917 1918 1919 1920
## 79.23893 81.76145 81.14395 85.10189 80.91431 81.42248 85.01924 85.42600
## 1921 1922 1923 1924 1925 1926 1927 1928
## 83.96663 80.85756 80.44941 80.30771 82.18010 80.78887 75.54209 76.41022
## 1929 1930 1931 1932 1933 1934 1935 1936
## 77.23605 77.21864 76.19820 76.05683 75.75244 74.46674 70.71020 70.68491
## 1937 1938 1939 1940 1941 1942 1943 1944
## 72.66134 71.98177 71.56340 73.70976 71.23121 65.25482 63.15032 62.79318
## 1945 1946 1947 1948 1949 1950 1951 1952
## 62.48705 62.28178 63.46560 63.25874 63.00474 62.28478 61.68213 60.76199
## 1953 1954 1955 1956 1957 1958 1959 1960
## 63.51657 59.72414 59.57795 59.39208 59.16499 62.11241 78.20699 72.76947
## 1961 1962 1963 1964 1965 1966 1967 1968
## 72.70416 72.54950 73.70515 73.16806 74.33424 71.79010 71.66359 71.33360
## 1969 1970 1971 1972 1973 1974 1975 1976
## 73.03325 70.87939 73.77135 73.61317 73.39673 73.03655 72.70858 64.31285
## 1977 1978 1979 1980 1981 1982 1983 1984
## 64.17437 63.98624 63.68206 63.60210 63.21519 62.78015 66.98840 61.85830
## 1985 1986 1987 1988 1989 1990 1991 1992
## 61.41722 65.72762 59.28729 60.00025 59.37853 59.25520 58.71018 69.26677
## 1993 1994 1995 1996 1997 1998 1999 2000
## 70.33276 69.77801 69.76240 72.49038 69.96654 69.61317 69.14092 71.49164
## 2001 2002 2003 2004 2005 2006 2007 2008
## 71.35263 71.43874 71.11687 69.32220 67.52400 71.17047 68.26475 71.92409
## 2009 2010 2011 2012 2013 2014 2015 2016
## 72.11275 72.04941 74.24509 74.02791 75.71472 75.79712 71.59029 71.77371
## 2017 2018 2019 2020 2021 2022 2023 2024
## 73.11153 70.46929 70.15816 72.75528 73.35551 70.60083 72.75613 67.51778
## 2025 2026 2027 2028 2029 2030 2031 2032
## 66.34069 67.11953 67.14911 66.93936 66.78702 67.05874 69.25046 66.72942
## 2033 2034 2035 2036 2037 2038 2039 2040
## 66.06361 66.00912 66.55109 66.36883 66.11952 66.13252 66.09617 79.09451
## 2041 2042 2043 2044 2045 2046 2047 2048
## 80.96310 77.47155 77.86383 77.87099 79.54711 77.26241 78.73515 76.37475
## 2049 2050 2051 2052 2053 2054 2055 2056
## 76.25174 76.07023 76.91511 76.68138 76.30399 75.90198 75.64077 79.57556
## 2057 2058 2059 2060 2061 2062 2063 2064
## 77.70179 78.12227 79.09788 79.45283 79.12712 79.51425 79.32691 77.79999
## 2065 2066 2067 2068 2069 2070 2071 2072
## 78.54986 79.97927 77.96899 79.98886 79.82913 78.01112 77.28136 79.33503
## 2073 2074 2075 2076 2077 2078 2079 2080
## 79.31643 77.48874 80.08534 79.03590 74.61731 77.31947 78.14478 74.94046
## 2081 2082 2083 2084 2085 2086 2087 2088
## 76.12308 78.27757 77.65021 76.65078 74.52817 74.77719 75.40081 77.92914
## 2089 2090 2091 2092 2093 2094 2095 2096
## 77.27097 76.63965 76.40950 76.41089 77.10431 77.75247 77.69053 77.27661
## 2097 2098 2099 2100 2101 2102 2103 2104
## 75.91095 76.19937 71.73455 75.09738 74.06098 76.36143 72.47528 70.56301
## 2105 2106 2107 2108 2109 2110 2111 2112
## 71.41432 70.97114 73.28654 70.16663 62.81347 68.87409 70.77485 70.04549
## 2113 2114 2115 2116 2117 2118 2119 2120
## 70.42779 70.82814 70.65842 71.01787 70.03548 70.08595 68.23851 72.53474
## 2121 2122 2123 2124 2125 2126 2127 2128
## 76.21858 75.11952 76.83320 74.41626 77.03173 76.22283 75.51425 75.32608
## 2129 2130 2131 2132 2133 2134 2135 2136
## 74.70679 74.18542 73.66156 73.03781 72.41304 72.06525 71.89956 72.84244
## 2137 2138 2139 2140 2141 2142 2143 2144
## 74.85035 74.56699 73.99959 73.57001 72.44076 72.90578 72.54337 71.74775
## 2145 2146 2147 2148 2149 2150 2151 2152
## 76.61998 70.93875 70.62261 70.29376 70.17110 74.60857 74.28368 66.87084
## 2153 2154 2155 2156 2157 2158 2159 2160
## 69.81450 66.00649 66.10967 65.32445 68.52055 63.65107 63.38418 62.20298
## 2161 2162 2163 2164 2165 2166 2167 2168
## 59.86831 64.38642 54.67592 62.45794 53.01401 52.40322 51.87391 73.51837
## 2169 2170 2171 2172 2173 2174 2175 2176
## 73.23830 73.31946 73.26266 73.27256 73.00394 72.87343 72.62966 72.37554
## 2177 2178 2179 2180 2181 2182 2183 2184
## 72.46286 68.33897 74.08590 71.47275 70.57510 69.07490 71.36953 63.85532
## 2185 2186 2187 2188 2189 2190 2191 2192
## 73.47245 73.34016 73.09659 73.31449 74.01654 72.88956 72.76642 72.70931
## 2193 2194 2195 2196 2197 2198 2199 2200
## 75.20976 72.32815 72.28243 71.87875 71.61543 71.55345 71.05121 64.80471
## 2201 2202 2203 2204 2205 2206 2207 2208
## 72.27503 72.16175 72.06858 71.86242 71.77039 71.61551 70.94082 71.31570
## 2209 2210 2211 2212 2213 2214 2215 2216
## 68.94425 68.62578 73.31174 70.46741 70.10394 69.87294 69.68358 74.77597
## 2217 2218 2219 2220 2221 2222 2223 2224
## 75.13546 71.04075 67.85665 68.74658 68.19070 67.71066 70.78288 70.17293
## 2225 2226 2227 2228 2229 2230 2231 2232
## 66.88609 66.63893 69.96924 65.60561 65.80970 65.69877 65.12783 63.42327
## 2233 2234 2235 2236 2237 2238 2239 2240
## 62.13132 77.81134 78.59784 77.97745 77.66352 75.55963 75.74819 74.62742
## 2241 2242 2243 2244 2245 2246 2247 2248
## 74.19845 74.75470 74.33131 73.92927 75.57017 75.35809 75.17009 75.01769
## 2249 2250 2251 2252 2253 2254 2255 2256
## 74.91810 63.90478 63.47489 63.89358 67.51133 66.67809 62.21666 61.81621
## 2257 2258 2259 2260 2261 2262 2263 2264
## 60.62217 65.52827 59.87020 59.55348 59.24086 58.80622 58.26270 57.79389
## 2265 2266 2267 2268 2269 2270 2271 2272
## 62.00025 73.74016 75.04072 75.13580 75.39102 74.89814 74.47284 74.81584
## 2273 2274 2275 2276 2277 2278 2279 2280
## 73.97970 74.11274 74.29965 73.97416 72.86170 71.26005 73.76464 73.45245
## 2281 2282 2283 2284 2285 2286 2287 2288
## 73.10365 73.47361 75.10493 73.21160 73.02474 72.60559 74.73290 71.75175
## 2289 2290 2291 2292 2293 2294 2295 2296
## 72.17409 72.09471 70.55433 69.62966 70.75289 70.95046 70.87186 70.90246
## 2297 2298 2299 2300 2301 2302 2303 2304
## 65.60508 59.82485 58.89737 68.27629 61.45158 58.54257 57.48755 57.66869
## 2305 2306 2307 2308 2309 2310 2311 2312
## 55.89830 62.63269 55.59004 63.30591 55.08589 62.73573 54.41007 54.81570
## 2313 2314 2315 2316 2317 2318 2319 2320
## 54.40861 80.88678 80.82747 78.33113 80.59008 81.25141 79.23348 78.74442
## 2321 2322 2323 2324 2325 2326 2327 2328
## 78.52492 77.33655 76.63243 75.23947 74.91332 75.88382 74.69644 75.64449
## 2329 2330 2331 2332 2333 2334 2335 2336
## 75.49152 79.29961 77.62396 77.44581 77.30493 77.10142 77.30407 76.93436
## 2337 2338 2339 2340 2341 2342 2343 2344
## 76.64224 78.36844 75.99344 75.57970 75.32109 74.99037 74.65191 74.50929
## 2345 2346 2347 2348 2349 2350 2351 2352
## 72.59405 78.17417 80.49653 79.84020 80.71885 80.92762 80.66491 82.07443
## 2353 2354 2355 2356 2357 2358 2359 2360
## 79.37514 81.72167 81.30881 80.91154 78.54059 77.97128 78.01375 76.57676
## 2361 2362 2363 2364 2365 2366 2367 2368
## 76.43920 66.89612 67.36399 68.17010 68.07314 67.95112 66.92420 67.76765
## 2369 2370 2371 2372 2373 2374 2375 2376
## 66.53995 69.72607 70.09505 67.22795 66.82998 62.06520 66.22439 61.94317
## 2377 2378 2379 2380 2381 2382 2383 2384
## 62.20446 59.95647 60.43347 60.25911 59.77481 59.84630 59.46589 55.82502
## 2385 2386 2387 2388 2389 2390 2391 2392
## 58.47587 60.67799 51.64523 49.97989 51.82865 56.05160 56.42783 56.84529
## 2393 2394 2395 2396 2397 2398 2399 2400
## 56.74133 65.58428 63.64717 64.20860 68.37565 60.98972 59.45851 55.14164
## 2401 2402 2403 2404 2405 2406 2407 2408
## 52.57373 50.84075 50.35211 48.89529 48.71297 49.21261 50.69843 51.20503
## 2409 2410 2411 2412 2413 2414 2415 2416
## 52.92688 55.67836 55.86992 55.41743 55.20245 55.16905 48.24395 48.06013
## 2417 2418 2419 2420 2421 2422 2423 2424
## 48.58448 47.49094 47.59652 47.60569 47.38239 47.60908 47.81217 48.11315
## 2425 2426 2427 2428 2429 2430 2431 2432
## 53.93787 82.52165 81.03272 81.95283 81.91833 81.70466 79.94205 81.16648
## 2433 2434 2435 2436 2437 2438 2439 2440
## 82.12306 79.25478 80.30037 76.87396 79.68144 79.37098 78.43257 79.02414
## 2441 2442 2443 2444 2445 2446 2447 2448
## 78.89385 72.52322 72.22856 72.00265 71.84968 71.08488 71.76383 70.70478
## 2449 2450 2451 2452 2453 2454 2455 2456
## 70.76508 71.16634 71.06270 70.95474 69.68513 70.45908 70.31385 72.48122
## 2457 2458 2459 2460 2461 2462 2463 2464
## 69.18485 63.73325 64.04176 63.46046 63.32850 63.71394 60.31928 60.52366
## 2465 2466 2467 2468 2469 2470 2471 2472
## 60.06135 59.82493 63.23195 59.24950 57.95184 57.96570 57.89831 57.72771
## 2473 2474 2475 2476 2477 2478 2479 2480
## 57.63722 70.57437 70.46728 70.41168 70.11981 70.03225 74.60181 69.17582
## 2481 2482 2483 2484 2485 2486 2487 2488
## 68.62456 71.63040 68.10565 71.15546 60.63524 61.87819 61.79977 61.74028
## 2489 2490 2491 2492 2493 2494 2495 2496
## 62.45659 60.19330 62.37980 60.95863 58.29488 54.53670 50.99029 52.30735
## 2497 2498 2499 2500 2501 2502 2503 2504
## 41.37872 48.40851 37.35786 43.43470 42.38610 42.95453 33.07959 34.01486
## 2505 2506 2507 2508 2509 2510 2511 2512
## 35.86702 80.11885 79.99787 79.93751 82.34759 82.57008 79.63940 79.56918
## 2513 2514 2515 2516 2517 2518 2519 2520
## 81.88497 81.78430 81.46997 79.50746 82.37148 80.83163 80.40397 80.18380
## 2521 2522 2523 2524 2525 2526 2527 2528
## 80.19991 80.65055 84.18023 83.99871 83.77222 83.86323 82.94343 83.45571
## 2529 2530 2531 2532 2533 2534 2535 2536
## 83.02247 81.55397 81.11236 80.93966 80.69487 78.16261 80.02112 79.79853
## 2537 2538 2539 2540 2541 2542 2543 2544
## 78.36861 63.52493 63.76873 71.97135 71.60909 69.01045 69.22688 69.33573
## 2545 2546 2547 2548 2549 2550 2551 2552
## 67.54300 69.03841 68.90490 68.40108 67.83627 67.50350 67.35548 67.19553
## 2553 2554 2555 2556 2557 2558 2559 2560
## 67.05804 69.08716 70.30175 70.12383 69.99484 69.85896 69.72046 69.59889
## 2561 2562 2563 2564 2565 2566 2567 2568
## 66.75600 66.70124 66.45219 66.12749 66.23522 65.63735 65.13838 64.97119
## 2569 2570 2571 2572 2573 2574 2575 2576
## 64.76403 72.85263 72.75739 72.61757 71.56140 72.06727 71.50138 73.94524
## 2577 2578 2579 2580 2581 2582 2583 2584
## 71.13155 70.45037 70.34951 69.77624 69.35894 68.46437 67.82555 68.17848
## 2585 2586 2587 2588 2589 2590 2591 2592
## 67.81903 74.23137 76.04932 75.95469 75.91061 75.79500 75.88400 74.15665
## 2593 2594 2595 2596 2597 2598 2599 2600
## 73.35345 75.11158 73.00564 69.58618 69.57102 67.57540 67.48097 67.37977
## 2601 2602 2603 2604 2605 2606 2607 2608
## 67.33268 68.06542 68.05441 67.33192 67.31544 67.09612 66.95405 66.67213
## 2609 2610 2611 2612 2613 2614 2615 2616
## 66.00749 65.36757 64.66699 67.08436 63.07485 66.44557 62.20835 62.01065
## 2617 2618 2619 2620 2621 2622 2623 2624
## 50.65446 64.02925 63.92954 63.59847 63.30517 67.03857 60.82922 59.36445
## 2625 2626 2627 2628 2629 2630 2631 2632
## 58.50753 59.36051 59.00841 58.65210 58.52705 58.28753 58.10815 57.88698
## 2633 2634 2635 2636 2637 2638 2639 2640
## 57.94187 73.05529 73.16817 73.12254 72.95017 75.10877 72.91684 72.69016
## 2641 2642 2643 2644 2645 2646 2647 2648
## 72.85135 70.53076 70.51294 75.17374 74.04427 73.15324 71.51730 72.62894
## 2649 2650 2651 2652 2653 2654 2655 2656
## 73.78520 74.49255 73.29581 72.37381 72.97508 71.16858 71.67627 69.56814
## 2657 2658 2659 2660 2661 2662 2663 2664
## 70.28306 68.93246 69.66732 71.60926 73.63385 70.59509 69.66857 70.12388
## 2665 2666 2667 2668 2669 2670 2671 2672
## 67.39568 77.30632 75.21137 77.12651 76.98156 76.85283 76.52098 76.61810
## 2673 2674 2675 2676 2677 2678 2679 2680
## 76.26366 76.35079 76.17891 75.81085 75.45326 73.59774 74.94084 74.82915
## 2681 2682 2683 2684 2685 2686 2687 2688
## 72.70500 77.48136 77.78956 77.49844 75.28373 75.22099 73.91498 73.43927
## 2689 2690 2691 2692 2693 2694 2695 2696
## 71.31136 72.99459 70.15771 70.20617 69.74326 69.80621 69.08282 70.60646
## 2697 2698 2699 2700 2701 2702 2703 2704
## 68.18333 70.04001 69.89930 69.18138 73.05545 69.36864 64.41775 64.04114
## 2705 2706 2707 2708 2709 2710 2711 2712
## 63.65983 63.43496 63.47789 61.94620 62.20111 61.22899 63.46464 63.59638
## 2713 2714 2715 2716 2717 2718 2719 2720
## 55.51402 61.82786 61.17200 65.76322 60.07601 59.62423 59.04049 58.40697
## 2721 2722 2723 2724 2725 2726 2727 2728
## 57.76047 63.49138 63.02415 63.06425 56.05948 55.75721 62.42708 52.86447
## 2729 2730 2731 2732 2733 2734 2735 2736
## 51.96834 50.49794 72.41242 73.32636 70.20583 75.02511 75.00300 71.62780
## 2737 2738 2739 2740 2741 2742 2743 2744
## 71.24075 71.83388 72.18679 71.37298 71.72101 71.91472 71.78753 71.26057
## 2745 2746 2747 2748 2749 2750 2751 2752
## 70.48148 70.81644 75.71877 77.66175 73.66242 78.59751 75.43556 75.35182
## 2753 2754 2755 2756 2757 2758 2759 2760
## 75.27223 77.10225 76.73252 76.59464 76.23419 75.84386 74.10077 76.76732
## 2761 2762 2763 2764 2765 2766 2767 2768
## 75.19873 74.90035 82.29360 82.09664 82.72755 82.45962 81.61136 82.04951
## 2769 2770 2771 2772 2773 2774 2775 2776
## 82.25451 82.82571 84.06430 82.02273 78.57717 78.13549 80.83331 81.39110
## 2777 2778 2779 2780 2781 2782 2783 2784
## 79.70910 79.61191 65.00993 69.44566 62.93047 61.52239 58.97841 64.08974
## 2785 2786 2787 2788 2789 2790 2791 2792
## 55.12295 56.18969 53.69256 53.57208 49.23853 54.96892 50.37235 59.10981
## 2793 2794 2795 2796 2797 2798 2799 2800
## 56.58835 49.99795 83.33307 80.77121 81.35467 80.56111 82.51971 81.20597
## 2801 2802 2803 2804 2805 2806 2807 2808
## 81.57364 80.48049 81.51717 79.40264 78.23872 79.32635 78.95135 77.16557
## 2809 2810 2811 2812 2813 2814 2815 2816
## 74.23293 73.72361 77.66880 77.59992 77.57136 76.77118 77.44149 77.24814
## 2817 2818 2819 2820 2821 2822 2823 2824
## 75.05215 74.69525 76.12006 76.54463 76.37080 76.53247 75.82472 75.38663
## 2825 2826 2827 2828 2829 2830 2831 2832
## 75.24578 74.02310 71.43112 71.22383 71.06073 70.99733 70.93319 69.40162
## 2833 2834 2835 2836 2837 2838 2839 2840
## 69.29010 70.46429 70.24019 70.11961 69.87465 69.89464 69.58508 69.28826
## 2841 2842 2843 2844 2845 2846 2847 2848
## 68.99224 64.43630 70.71784 68.58311 68.43386 66.70706 68.26308 68.18473
## 2849 2850 2851 2852 2853 2854 2855 2856
## 67.93751 67.77504 67.63101 67.30822 63.00585 62.99216 62.57924 62.35977
## 2857 2858 2859 2860 2861 2862 2863 2864
## 62.19685 64.64516 72.59896 72.39142 72.38618 70.20801 72.05802 72.11060
## 2865 2866 2867 2868 2869 2870 2871 2872
## 71.87098 71.25507 70.74990 70.40186 69.73552 69.39352 69.17490 68.72663
## 2873 2874 2875 2876 2877 2878 2879 2880
## 68.15328 68.28720 70.93281 70.52026 69.55319 72.39850 69.99990 69.73805
## 2881 2882 2883 2884 2885 2886 2887 2888
## 69.46026 69.28154 69.09259 68.82034 68.56944 68.09888 67.83200 66.60234
## 2889 2890 2891 2892 2893 2894 2895 2896
## 67.63900 67.27937 63.45242 62.02831 63.34538 63.08494 62.71426 62.64522
## 2897 2898 2899 2900 2901 2902 2903 2904
## 62.45907 62.43100 66.25528 62.28339 62.09456 61.71411 61.54815 65.40294
## 2905 2906 2907 2908 2909 2910 2911 2912
## 61.26469 60.99697 68.10108 62.99530 62.36775 61.39485 60.14202 58.99516
## 2913 2914 2915 2916 2917 2918 2919 2920
## 60.15632 62.60483 53.46683 51.47682 50.29597 49.27673 57.84015 56.88280
## 2921 2922 2923 2924 2925 2926 2927 2928
## 47.02864 46.47385 59.73936 61.43472 59.69966 57.54467 55.82418 50.72720
## 2929 2930 2931 2932 2933 2934 2935 2936
## 48.43725 46.26522 54.59572 54.04709 39.56237 37.79854 36.67575 47.67924
## 2937 2938
## 35.44955 34.54925actual = life_exp1$Life.expectancy
actual## [1] 65.0 59.9 59.9 59.5 59.2 58.8 58.6 58.1 57.5 57.3 57.3 57.0 56.7 56.2
## [15] 55.3 54.8 77.8 77.5 77.2 76.9 76.6 76.2 76.1 75.3 75.9 74.2 73.5 73.0
## [29] 72.8 73.3 73.6 72.6 75.6 75.4 75.3 75.1 74.9 74.7 74.4 74.1 73.8 73.4
## [43] 72.9 72.3 71.7 71.6 71.4 71.3 52.4 51.7 51.1 56.0 51.0 49.6 49.1 48.7
## [57] 48.2 47.7 47.4 47.1 46.8 46.5 45.7 45.3 76.4 76.2 76.1 75.9 75.7 75.6
## [71] 75.4 75.2 75.0 74.8 74.6 74.4 74.2 74.0 73.8 73.6 76.3 76.2 76.0 75.9
## [85] 75.7 75.5 75.6 75.4 74.8 75.2 74.9 74.7 74.1 74.1 74.0 74.1 74.8 74.6
## [99] 74.4 74.4 73.9 73.5 73.3 73.2 73.5 72.9 73.0 73.0 72.7 72.6 72.6 72.0
## [113] 82.8 82.7 82.5 82.3 82.0 81.9 81.7 81.3 81.3 81.2 81.0 86.0 83.0 79.9
## [127] 79.9 79.5 81.5 81.4 81.1 88.0 88.0 84.0 82.0 84.0 81.0 79.8 79.4 79.3
## [141] 78.8 78.7 78.6 78.1 72.7 72.5 72.2 71.9 71.6 71.1 78.0 73.0 73.0 69.2
## [155] 68.4 68.4 67.8 67.8 67.5 66.6 76.1 75.4 74.8 74.9 75.0 75.0 74.6 74.5
## [169] 74.4 74.2 74.1 73.8 73.2 73.1 72.9 72.6 76.9 76.8 76.7 76.5 76.1 76.1
## [183] 76.0 75.8 75.6 75.5 75.3 75.2 75.0 74.9 74.7 74.5 71.8 71.4 71.0 77.0
## [197] 73.0 69.9 69.5 69.1 68.6 68.2 67.8 67.3 66.8 66.3 65.8 65.3 75.5 75.4
## [211] 75.2 75.1 74.9 74.7 74.6 74.4 74.2 74.1 73.9 73.8 73.7 73.5 73.4 73.3
## [225] 72.3 72.0 71.7 71.9 72.0 73.0 70.0 70.0 69.8 68.9 68.1 68.2 67.7 67.2
## [239] 67.7 68.0 81.1 89.0 87.0 83.0 83.0 80.0 79.8 79.5 79.5 79.4 78.9 78.8
## [253] 78.3 78.0 78.0 77.6 71.0 70.0 69.8 69.4 69.4 69.5 69.5 69.6 69.6 69.4
## [267] 69.0 68.7 68.4 68.5 68.2 68.3 60.0 59.7 59.5 59.3 59.1 58.7 58.4 57.6
## [281] 57.1 56.8 56.5 56.1 55.8 55.6 55.5 55.4 69.8 69.4 69.1 68.7 68.3 67.9
## [295] 67.4 67.0 66.5 65.8 65.0 64.2 63.3 62.5 61.7 62.0 77.0 74.0 71.0 69.8
## [309] 69.3 68.7 68.0 67.4 66.8 66.2 65.7 65.1 64.5 63.9 63.3 62.6 77.4 77.2
## [323] 77.0 76.8 76.9 76.4 76.1 76.0 75.4 75.7 75.0 75.5 75.2 75.4 74.9 74.6
## [337] 65.7 65.1 64.2 63.4 62.2 61.1 59.2 57.5 56.9 54.8 51.7 48.1 46.4 46.0
## [351] 46.7 47.8 75.0 74.8 74.7 74.5 74.1 73.8 73.6 73.4 73.3 73.0 72.7 72.0
## [365] 71.8 71.4 71.0 75.0 77.7 77.6 77.1 78.3 77.4 76.9 76.8 77.2 76.0 76.3
## [379] 76.2 76.4 76.0 74.8 74.7 74.4 74.5 74.3 74.1 73.9 73.7 73.4 73.2 72.9
## [393] 72.6 72.2 72.1 72.2 72.0 71.8 71.6 71.1 59.9 59.3 59.0 58.6 58.1 57.5
## [407] 56.9 56.1 55.3 54.3 53.3 52.4 51.6 51.0 56.0 51.0 59.6 59.1 58.6 58.0
## [421] 57.4 56.8 56.2 55.3 54.8 54.1 53.4 52.6 51.9 51.5 51.3 58.0 53.3 52.8
## [435] 52.3 52.0 51.7 51.5 51.0 54.0 49.9 49.4 48.7 48.2 48.0 47.7 47.8 47.9
## [449] 73.3 73.0 72.8 72.7 72.6 72.5 72.4 72.4 72.3 72.1 71.8 71.4 71.1 77.0
## [463] 73.0 69.9 68.7 68.3 67.8 67.4 67.0 66.6 66.1 65.6 65.0 64.1 62.9 61.5
## [477] 63.0 59.3 58.5 57.7 57.3 56.7 56.4 55.9 55.6 55.3 54.8 54.2 53.6 53.3
## [491] 52.8 52.1 51.8 51.6 51.5 51.4 82.2 82.0 81.8 81.6 81.5 81.2 81.0 87.0
## [505] 85.0 85.0 81.0 80.0 79.7 79.5 79.4 79.1 52.5 58.0 49.9 53.0 49.8 49.2
## [519] 48.6 47.6 46.8 46.3 45.9 45.7 45.7 45.6 45.6 46.0 53.1 52.6 52.2 51.8
## [533] 51.6 51.2 57.0 49.6 49.4 48.5 48.6 48.5 48.4 48.1 48.0 47.6 85.0 83.0
## [547] 81.0 79.9 79.8 79.1 79.3 79.6 78.9 78.9 78.4 78.0 77.9 77.8 77.3 77.3
## [561] 76.1 75.8 75.6 75.4 75.2 75.0 74.9 74.5 74.4 74.2 73.9 73.5 73.1 72.7
## [575] 72.2 71.7 74.8 74.6 74.4 74.3 74.2 73.6 73.6 73.5 73.5 73.1 73.1 72.8
## [589] 72.4 71.8 71.5 71.4 63.5 63.2 62.9 62.5 62.2 61.8 61.3 61.0 66.0 63.0
## [603] 60.0 59.8 59.6 59.5 59.5 59.5 64.7 64.2 63.9 63.7 62.9 62.0 68.0 59.4
## [617] 58.2 56.9 55.3 54.1 53.2 52.6 52.7 52.9 73.4 79.6 79.5 79.4 79.2 79.0
## [631] 78.1 79.2 78.9 78.9 78.0 78.6 77.7 78.0 78.3 77.5 77.6 78.0 77.8 77.7
## [645] 77.1 77.0 76.6 76.3 76.0 75.8 75.9 75.2 75.4 74.7 74.8 74.9 74.7 79.1
## [659] 79.0 78.7 78.7 78.8 78.0 78.1 77.9 78.1 78.0 77.2 77.3 77.4 77.7 76.7
## [673] 76.9 85.0 83.0 81.0 80.0 79.7 79.5 79.3 79.1 78.9 78.8 78.7 78.6 78.5
## [687] 78.4 78.2 78.1 78.8 78.6 78.2 78.0 77.8 77.5 77.1 77.0 76.8 76.5 75.9
## [701] 75.8 75.2 75.3 75.1 74.7 76.0 73.0 71.0 69.8 69.4 69.0 68.7 68.6 68.5
## [715] 68.5 68.5 68.4 68.1 67.6 66.6 65.4 59.8 59.3 58.8 58.3 57.9 57.4 56.7
## [729] 56.3 55.7 55.0 54.3 53.5 52.8 52.1 51.8 51.3 86.0 84.0 81.0 80.0 79.7
## [743] 79.2 78.9 78.8 78.4 78.1 78.1 77.7 77.3 77.0 77.0 76.9 63.5 63.0 62.7
## [757] 62.2 61.8 61.3 69.0 62.0 59.8 59.1 58.6 58.1 58.0 57.9 57.7 57.4 73.6
## [771] 73.9 73.6 73.4 72.1 73.1 72.7 73.6 73.3 72.9 72.3 69.7 69.3 73.0 71.4
## [785] 71.2 72.0 76.2 76.0 76.0 75.5 75.3 75.0 75.1 74.6 74.7 74.4 74.2 74.4
## [799] 74.4 73.6 73.4 72.8 79.0 78.0 79.0 72.0 74.0 70.0 69.9 69.8 69.7 69.5
## [813] 69.4 69.0 68.6 68.7 68.6 68.8 73.5 73.3 73.0 73.0 72.0 72.0 71.4 71.7
## [827] 71.2 75.0 71.0 70.0 69.9 73.0 68.9 69.0 58.2 57.9 57.4 56.7 56.2 56.1
## [841] 55.7 55.4 55.0 54.8 54.4 54.1 53.8 53.5 53.1 52.7 64.7 64.4 64.0 63.6
## [855] 62.9 62.1 61.4 67.0 62.0 59.7 59.4 59.1 58.8 58.5 58.1 45.3 77.6 77.3
## [869] 76.9 76.3 76.1 75.6 74.9 74.2 73.0 73.0 72.8 72.3 71.9 71.2 78.0 78.0
## [883] 64.8 64.2 63.7 63.3 62.6 61.8 68.0 59.8 58.5 57.2 56.0 55.0 54.0 53.2
## [897] 52.5 51.2 69.9 69.7 69.6 69.4 69.2 69.1 68.9 68.7 68.6 68.5 68.3 68.1
## [911] 68.0 67.9 67.8 67.7 81.1 89.0 87.0 84.0 83.0 79.9 79.7 79.6 79.3 79.2
## [925] 78.9 78.7 78.4 78.1 78.0 77.5 82.4 82.2 82.0 81.5 81.7 81.3 81.1 89.0
## [939] 89.0 86.0 81.0 82.0 79.3 79.2 79.0 78.8 66.0 65.5 64.6 63.5 62.8 62.3
## [953] 61.7 61.6 61.6 61.4 65.0 59.7 59.7 59.7 59.8 61.0 61.1 68.0 66.0 62.0
## [967] 59.8 59.3 59.0 58.7 58.5 58.2 57.7 57.3 57.0 56.6 56.3 55.9 74.4 74.5
## [981] 74.5 74.2 73.9 73.8 73.2 73.9 74.4 73.9 73.9 72.3 72.7 71.7 73.0 71.8
## [995] 81.0 89.0 86.0 86.0 85.0 81.0 80.0 79.9 79.8 79.6 79.2 79.1 78.5 78.4
## [1009] 78.3 78.0 62.4 62.1 61.9 61.6 61.2 69.0 66.0 63.0 59.9 59.4 58.9 58.3
## [1023] 57.9 57.6 57.4 57.2 81.0 88.0 86.0 84.0 85.0 83.0 80.0 79.9 79.4 79.7
## [1037] 79.3 79.2 79.1 79.0 78.7 78.2 73.6 73.5 73.3 73.1 72.9 72.6 72.4 72.1
## [1051] 71.9 71.7 71.5 73.0 71.1 79.0 77.0 74.0 71.9 71.7 71.4 71.3 71.1 77.0
## [1065] 76.0 79.0 75.0 69.7 69.2 69.6 69.4 69.3 68.4 67.7 59.0 58.1 58.8 58.4
## [1079] 58.1 57.8 57.3 56.8 56.4 55.6 54.7 54.0 53.3 52.9 52.5 52.5 58.9 58.4
## [1093] 58.1 57.6 57.1 56.7 56.3 55.6 55.0 54.4 53.9 53.5 53.0 52.8 52.5 52.1
## [1107] 66.2 66.0 65.9 65.8 65.6 65.9 66.1 66.3 65.7 65.2 65.0 65.1 65.3 65.3
## [1121] 65.4 65.4 63.5 63.1 62.7 62.3 62.3 36.3 62.5 62.1 61.8 61.1 65.0 58.7
## [1135] 59.7 59.3 58.9 58.6 74.6 74.5 74.3 74.1 73.9 73.6 73.4 73.2 73.0 72.8
## [1149] 72.5 72.2 71.9 71.6 71.3 71.0 75.8 75.6 75.5 75.0 74.8 74.5 74.2 74.1
## [1163] 73.5 73.4 72.9 72.9 72.5 72.5 72.3 71.7 82.7 82.5 82.4 82.5 82.1 81.8
## [1177] 81.6 81.4 81.3 81.1 81.0 88.0 87.0 84.0 80.0 79.7 68.3 68.0 67.6 67.3
## [1191] 66.8 66.4 66.0 65.5 65.2 64.8 64.4 64.0 63.7 63.3 62.9 62.5 69.1 68.9
## [1205] 68.7 68.5 68.3 68.1 67.9 67.7 67.5 67.3 67.2 65.3 66.9 66.7 66.5 66.3
## [1219] 75.5 75.4 75.3 75.1 74.7 74.1 73.3 72.7 72.4 72.2 72.0 71.8 75.0 71.2
## [1233] 78.0 73.0 68.9 67.9 69.5 76.0 77.0 76.0 74.0 69.3 65.9 64.7 66.8 67.2
## [1247] 66.5 74.0 72.0 70.0 81.4 81.2 81.0 85.0 84.0 86.0 79.7 79.8 79.5 79.0
## [1261] 78.7 78.3 78.0 77.4 77.0 76.4 82.5 82.2 82.1 81.8 81.8 81.7 81.5 81.0
## [1275] 84.0 84.0 80.0 81.0 79.7 79.3 79.3 78.9 82.7 82.5 82.3 82.0 82.0 81.8
## [1289] 81.6 81.5 81.3 81.2 88.0 89.0 79.9 80.0 79.8 79.4 76.2 75.8 75.6 75.3
## [1303] 75.2 75.0 74.7 74.5 74.2 74.0 73.5 73.3 73.1 73.0 72.7 72.6 83.7 83.5
## [1317] 83.5 83.3 82.5 83.0 83.0 82.7 82.6 82.4 82.0 82.1 81.9 81.8 81.5 81.1
## [1331] 74.1 74.0 73.9 73.7 73.6 73.4 73.3 73.1 73.0 72.8 72.4 72.5 72.3 72.1
## [1345] 71.9 71.7 72.0 69.9 69.5 69.1 68.5 67.8 67.8 66.6 65.3 65.0 64.6 64.7
## [1359] 64.4 64.7 64.4 63.9 63.4 62.9 62.6 62.1 61.2 63.0 59.1 57.9 56.8 55.3
## [1373] 54.1 53.0 52.4 52.1 51.9 51.9 66.3 66.1 65.8 65.7 65.5 65.3 65.2 65.1
## [1387] 65.0 65.0 64.9 64.8 64.7 64.6 64.3 64.1 74.7 74.6 74.5 74.3 74.2 74.0
## [1401] 73.9 73.8 73.7 73.6 73.6 73.5 73.4 73.3 73.2 73.2 71.1 78.0 77.0 69.9
## [1415] 69.4 68.8 68.5 67.6 67.2 66.7 66.9 67.1 66.6 66.7 67.2 66.6 65.7 65.3
## [1429] 64.9 64.4 64.0 63.6 63.1 62.6 62.1 61.5 61.0 64.0 59.8 59.3 58.7 58.1
## [1443] 74.6 74.4 74.1 73.8 73.6 72.8 72.6 71.9 78.0 75.0 76.0 71.0 78.0 73.0
## [1457] 69.9 71.0 74.9 74.8 74.9 75.0 75.0 74.9 74.7 74.5 74.4 74.1 73.9 73.7
## [1471] 73.5 73.2 73.0 72.7 53.7 52.1 52.1 52.2 52.3 51.1 49.4 47.8 46.2 45.3
## [1485] 44.5 44.8 45.5 46.4 47.8 49.3 61.4 58.1 61.1 67.0 62.0 59.7 59.2 58.6
## [1499] 57.9 56.7 55.3 54.0 50.0 56.0 51.5 51.9 72.7 72.4 72.9 72.9 71.3 72.8
## [1513] 72.7 72.6 72.5 72.2 71.9 71.5 71.3 71.1 71.0 78.0 73.6 73.4 73.0 73.0
## [1527] 72.8 72.4 72.2 71.1 72.0 76.0 78.0 71.6 71.6 71.4 71.2 71.6 82.0 81.7
## [1541] 81.4 81.1 88.0 86.0 83.0 80.0 79.7 79.4 78.8 78.7 78.6 78.3 78.0 77.8
## [1555] 65.5 65.1 64.7 64.3 63.8 63.3 62.8 62.3 61.9 61.4 69.0 64.0 59.9 59.3
## [1569] 58.7 57.9 58.3 57.6 56.7 55.3 54.1 52.9 51.5 50.0 48.5 47.1 46.0 45.1
## [1583] 44.6 44.0 43.5 43.1 75.0 74.8 74.6 74.5 74.3 74.1 74.0 73.8 73.7 73.6
## [1597] 73.4 73.2 73.1 72.9 72.7 72.4 78.5 78.2 77.9 77.6 77.3 76.7 76.3 75.9
## [1611] 75.4 75.0 74.3 73.4 72.7 71.8 78.0 69.6 58.2 57.8 57.3 57.2 56.8 56.5
## [1625] 56.0 55.5 55.0 54.3 53.6 52.8 52.0 51.2 55.0 49.8 81.7 81.4 81.1 81.0
## [1639] 87.0 83.0 82.0 80.0 79.6 79.3 79.0 78.7 78.5 78.2 77.8 77.5 72.2 63.1
## [1653] 63.0 62.7 62.5 62.2 62.0 61.7 61.4 61.2 69.0 66.0 64.0 63.0 62.0 61.0
## [1667] 60.0 74.6 74.2 74.1 73.9 73.6 73.3 72.8 72.7 72.9 71.8 72.1 71.9 71.5
## [1681] 71.5 71.5 71.0 76.7 76.6 76.6 76.3 76.1 75.6 75.7 75.6 76.0 75.8 75.3
## [1695] 75.4 75.0 75.0 75.0 74.8 69.4 69.4 69.2 69.0 68.9 68.7 68.5 68.4 68.2
## [1709] 68.0 67.9 67.7 67.5 66.2 67.2 67.0 77.0 68.8 68.4 68.1 67.8 67.3 66.3
## [1723] 66.9 67.4 65.9 65.0 64.5 64.0 64.0 63.8 63.2 62.8 76.1 75.9 75.8 75.6
## [1737] 75.4 75.3 75.0 74.6 74.2 73.8 73.6 73.5 73.5 73.4 73.3 73.0 74.3 74.1
## [1751] 73.9 73.6 73.3 72.8 72.3 71.8 71.4 71.0 77.0 72.0 69.9 69.5 69.0 68.6
## [1765] 57.6 56.7 55.3 54.8 54.3 54.0 53.8 53.2 52.1 51.2 58.0 54.0 51.0 49.8
## [1779] 49.5 49.0 66.6 66.4 66.2 65.9 65.6 65.4 65.2 59.2 64.5 64.2 63.9 63.5
## [1793] 63.2 62.8 62.5 62.1 65.8 65.9 66.1 65.8 64.3 63.0 62.4 61.7 60.0 57.0
## [1807] 55.1 54.7 55.0 55.7 56.5 57.4 72.8 69.2 69.6 69.3 68.9 68.4 68.0 67.5
## [1821] 67.0 66.6 66.0 65.4 64.7 64.3 63.1 63.2 62.5 81.9 81.7 81.4 81.1 81.1
## [1835] 88.0 86.0 83.0 82.0 79.8 79.4 79.2 78.7 78.4 78.3 78.1 81.6 81.5 81.3
## [1849] 81.1 86.0 89.0 85.0 81.0 81.0 79.9 79.9 79.2 79.1 78.7 78.5 78.6 74.8
## [1863] 74.5 73.9 73.9 74.5 73.2 73.2 72.5 72.5 73.0 71.2 71.0 76.0 75.0 73.0
## [1877] 73.0 61.8 61.4 69.0 63.0 59.4 58.2 57.1 56.0 55.2 54.5 53.7 52.9 52.1
## [1891] 51.4 56.0 50.0 54.5 53.6 53.2 52.7 52.3 52.0 51.6 59.0 55.0 49.8 49.2
## [1905] 48.5 48.1 47.7 47.4 47.1 77.0 81.8 81.6 81.5 81.3 81.1 81.0 89.0 86.0
## [1919] 85.0 84.0 81.0 79.8 79.4 78.9 78.8 78.5 76.6 76.4 76.2 76.0 75.8 75.6
## [1933] 75.4 75.2 74.9 74.7 74.3 74.0 73.6 73.3 72.9 72.6 66.4 66.2 66.0 65.7
## [1947] 65.5 65.1 64.8 64.6 64.4 64.2 62.9 63.7 63.5 63.2 63.0 62.8 79.0 77.8
## [1961] 77.6 77.5 77.2 77.3 76.5 76.8 76.5 76.4 76.2 75.8 75.8 75.5 75.7 75.5
## [1975] 75.7 62.9 62.7 62.4 62.2 62.0 61.8 61.6 61.4 61.1 68.0 64.0 59.9 59.6
## [1989] 59.3 59.1 58.9 74.0 73.9 73.8 73.6 73.4 73.2 73.0 72.7 72.5 72.3 72.1
## [2003] 71.9 71.7 71.5 71.2 79.0 75.5 75.3 75.3 74.9 74.5 73.7 73.8 73.9 74.0
## [2017] 74.2 72.8 72.2 72.1 72.6 72.4 71.4 68.5 68.4 68.1 68.1 68.0 67.9 68.0
## [2031] 67.5 67.5 67.3 67.0 67.3 67.2 66.8 66.8 66.8 77.5 77.3 77.1 76.8 76.7
## [2045] 76.3 75.7 75.5 75.3 75.2 75.0 74.9 74.7 74.5 74.2 73.7 81.1 89.0 86.0
## [2059] 83.0 82.0 79.6 79.3 79.0 78.7 78.5 77.7 78.0 77.3 77.2 76.9 76.6 78.2
## [2073] 78.1 77.9 77.8 77.5 77.3 77.0 76.8 76.7 76.6 76.6 76.6 76.5 76.4 76.3
## [2087] 76.2 82.3 82.0 81.7 81.2 81.1 87.0 86.0 83.0 79.8 79.4 78.7 78.2 77.6
## [2101] 77.1 76.7 76.0 72.1 71.8 71.7 79.0 77.0 68.8 69.0 68.9 68.3 68.0 67.3
## [2115] 68.0 67.6 67.5 67.6 67.1 75.0 74.8 74.6 74.4 74.3 73.4 73.1 73.1 72.9
## [2129] 72.5 71.9 71.7 71.1 77.0 78.0 77.0 75.0 73.0 70.0 69.6 69.4 68.4 68.2
## [2143] 67.5 67.3 66.4 65.0 64.9 64.6 64.8 65.1 65.0 66.1 65.7 65.2 64.6 63.8
## [2157] 62.8 61.0 68.0 59.6 57.6 55.3 53.4 52.0 57.0 48.6 48.3 76.8 75.2 75.0
## [2171] 74.8 74.7 74.6 74.2 74.3 74.1 73.9 73.5 73.1 72.6 72.2 72.0 71.8 71.6
## [2185] 73.2 73.1 72.7 72.8 72.7 72.5 72.3 72.1 71.9 71.7 71.4 71.2 71.0 79.0
## [2199] 79.0 79.0 74.0 73.8 73.6 73.2 73.0 72.6 76.0 72.5 72.2 72.0 71.6 71.4
## [2213] 79.0 76.0 75.0 72.0 78.6 67.5 67.3 67.1 66.9 66.6 66.2 65.8 65.4 65.1
## [2227] 64.7 64.3 63.8 63.4 63.1 62.8 62.6 74.5 74.4 74.3 74.1 73.9 73.7 73.4
## [2241] 73.3 73.2 73.2 73.1 73.1 73.0 72.9 72.8 72.6 66.7 66.4 66.0 65.6 64.9
## [2255] 64.3 63.5 62.8 62.1 61.3 65.0 59.7 59.0 58.4 57.9 57.5 75.6 75.4 75.3
## [2269] 74.9 74.6 74.4 74.1 74.0 73.8 73.6 73.0 73.0 73.0 72.9 73.1 72.6 73.2
## [2283] 73.0 72.9 72.7 72.6 72.4 72.3 72.2 72.2 72.2 72.2 72.1 72.1 72.1 72.0
## [2297] 71.8 51.0 48.1 54.0 49.7 48.9 48.1 47.1 46.2 45.3 44.3 43.3 42.3 41.5
## [2311] 48.0 41.0 39.0 83.1 82.9 82.7 82.5 82.2 82.0 81.7 81.4 81.1 87.0 82.0
## [2325] 79.7 79.3 79.0 78.7 78.3 76.7 76.4 76.1 75.8 75.6 75.1 75.0 74.7 74.4
## [2339] 74.3 74.0 74.1 73.8 73.7 73.3 73.0 88.0 87.0 85.0 82.0 79.8 79.5 79.1
## [2353] 78.9 78.3 78.1 77.5 77.2 76.5 76.6 76.2 76.0 69.2 68.8 68.8 68.7 68.5
## [2367] 68.3 68.1 68.0 67.6 67.6 67.4 67.1 66.8 66.5 66.2 65.8 55.0 54.3 54.2
## [2381] 53.1 53.1 52.4 52.2 51.9 51.5 51.5 51.6 51.2 51.1 58.0 57.0 55.0 62.9
## [2395] 62.0 69.0 59.2 58.9 58.0 56.5 55.3 54.5 54.0 53.8 53.7 54.0 54.9 56.0
## [2409] 57.3 57.3 56.6 56.4 56.0 55.4 55.0 54.3 53.6 53.1 52.5 51.9 51.4 58.0
## [2423] 52.0 49.6 48.9 82.8 82.6 82.4 82.0 82.1 81.9 81.6 81.3 89.0 88.0 81.0
## [2437] 81.0 79.4 79.5 79.4 79.1 74.9 74.7 74.6 74.5 74.5 74.5 71.8 72.3 73.7
## [2451] 73.8 74.2 69.1 73.9 73.7 72.7 71.5 64.1 63.8 63.5 63.2 62.7 62.5 62.0
## [2465] 61.8 61.4 61.0 67.0 59.7 59.6 59.4 58.9 58.6 71.6 71.4 71.2 71.3 76.0
## [2479] 73.0 70.0 69.8 69.5 69.3 68.9 68.3 68.0 67.9 67.7 67.4 58.9 58.4 57.6
## [2493] 56.5 55.0 53.6 52.6 51.4 50.0 47.8 46.0 45.6 45.9 46.4 47.1 48.4 82.4
## [2507] 82.3 81.9 81.7 81.7 81.5 81.4 81.1 89.0 88.0 85.0 83.0 82.0 79.9 79.8
## [2521] 79.6 83.4 83.2 83.0 82.7 82.6 82.3 82.1 82.0 81.7 81.5 81.1 81.0 85.0
## [2535] 84.0 82.0 79.7 64.5 64.4 63.6 62.8 71.7 73.7 73.8 73.8 73.8 73.7 73.5
## [2549] 73.2 73.0 72.8 72.7 72.6 69.7 69.6 69.3 68.8 68.1 67.3 66.7 66.4 66.1
## [2563] 65.9 65.5 65.9 65.2 64.3 64.0 63.7 74.9 74.6 74.5 74.3 74.1 73.9 73.7
## [2577] 73.5 73.3 73.0 72.5 71.6 71.7 71.4 71.2 71.1 75.7 75.5 75.3 75.1 74.9
## [2591] 74.7 74.4 74.2 73.5 73.7 73.6 73.5 73.2 72.8 73.1 72.6 68.3 68.0 67.7
## [2605] 67.4 67.2 66.9 66.6 66.2 65.8 64.9 63.7 62.3 61.0 62.0 59.4 58.7 59.9
## [2619] 59.7 59.4 58.9 58.3 57.4 56.7 56.2 55.9 55.7 55.0 54.9 54.7 54.7 54.6
## [2633] 54.6 73.5 73.3 73.2 73.0 72.9 72.8 72.5 72.6 72.5 72.4 72.3 72.2 72.0
## [2647] 71.9 71.8 71.6 71.2 71.1 71.0 78.0 76.0 74.0 71.0 69.9 69.7 69.6 69.5
## [2661] 69.4 69.3 69.2 69.1 69.1 75.3 75.1 74.9 74.9 74.8 74.8 74.7 74.7 74.6
## [2675] 74.4 74.2 74.0 73.7 73.5 73.2 72.9 75.8 75.5 75.2 74.8 74.5 74.2 73.9
## [2689] 73.5 73.2 72.8 72.4 72.0 71.6 71.2 78.0 74.0 66.3 66.0 65.4 65.6 65.6
## [2703] 65.8 65.6 64.5 64.1 63.7 63.3 63.5 63.4 63.3 64.0 63.8 71.9 62.3 61.5
## [2717] 67.0 60.0 59.3 58.4 57.5 56.3 55.5 54.9 53.2 51.3 51.0 48.8 47.7 46.6
## [2731] 71.3 78.0 71.0 77.0 75.0 69.8 69.2 67.7 67.5 67.7 67.0 67.4 67.6 67.6
## [2745] 67.7 67.5 77.1 76.9 76.7 76.5 76.3 76.2 76.0 75.8 75.6 75.4 75.3 75.1
## [2759] 74.9 74.7 74.5 74.2 81.2 81.0 87.0 86.0 86.0 82.0 81.0 79.6 79.5 79.3
## [2773] 79.0 78.8 78.3 78.2 78.0 77.8 61.8 67.0 59.7 58.6 58.3 57.5 56.9 56.2
## [2787] 54.5 53.1 52.2 51.5 58.0 52.0 49.6 49.2 79.3 79.1 78.9 78.8 78.7 78.7
## [2801] 78.5 78.2 78.1 77.8 77.5 77.5 77.2 77.0 76.9 76.8 77.0 76.8 76.8 76.5
## [2815] 77.0 76.3 76.6 76.4 75.4 76.2 75.7 75.4 75.4 75.4 75.2 75.1 69.4 69.2
## [2829] 69.1 68.8 68.5 68.3 68.0 67.9 67.8 67.6 67.3 67.8 67.2 67.1 67.4 67.1
## [2843] 72.0 71.7 71.6 71.4 71.2 71.0 78.0 75.0 73.0 71.0 69.9 69.6 69.4 69.3
## [2857] 69.1 69.0 74.1 73.9 73.8 73.7 73.8 73.7 73.6 73.2 73.4 73.6 73.6 73.3
## [2871] 72.4 73.1 72.5 72.5 76.0 75.9 75.7 75.6 75.4 75.2 75.0 74.9 74.7 74.6
## [2885] 74.4 74.2 74.0 73.8 73.6 73.4 65.7 65.4 65.4 64.7 64.6 64.4 64.1 63.8
## [2899] 63.4 63.0 62.6 62.2 61.9 61.5 61.1 68.0 61.8 61.1 63.0 59.2 58.2 58.0
## [2913] 57.4 55.7 52.6 58.0 49.3 47.9 46.4 45.5 44.6 43.8 67.0 59.2 58.0 56.6
## [2927] 54.9 52.4 50.0 48.2 46.6 45.4 44.6 44.3 44.5 44.8 45.3 46.0Backtrack=data.frame(actual, predicted)
Backtrack## actual predicted
## 1 65.0 62.53524
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## 1973 75.7 73.39673
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## 1977 62.7 64.17437
## 1978 62.4 63.98624
## 1979 62.2 63.68206
## 1980 62.0 63.60210
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## 1984 61.1 61.85830
## 1985 68.0 61.41722
## 1986 64.0 65.72762
## 1987 59.9 59.28729
## 1988 59.6 60.00025
## 1989 59.3 59.37853
## 1990 59.1 59.25520
## 1991 58.9 58.71018
## 1992 74.0 69.26677
## 1993 73.9 70.33276
## 1994 73.8 69.77801
## 1995 73.6 69.76240
## 1996 73.4 72.49038
## 1997 73.2 69.96654
## 1998 73.0 69.61317
## 1999 72.7 69.14092
## 2000 72.5 71.49164
## 2001 72.3 71.35263
## 2002 72.1 71.43874
## 2003 71.9 71.11687
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## 2005 71.5 67.52400
## 2006 71.2 71.17047
## 2007 79.0 68.26475
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## 2010 75.3 72.04941
## 2011 74.9 74.24509
## 2012 74.5 74.02791
## 2013 73.7 75.71472
## 2014 73.8 75.79712
## 2015 73.9 71.59029
## 2016 74.0 71.77371
## 2017 74.2 73.11153
## 2018 72.8 70.46929
## 2019 72.2 70.15816
## 2020 72.1 72.75528
## 2021 72.6 73.35551
## 2022 72.4 70.60083
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## 2024 68.5 67.51778
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## 2742 67.4 71.91472
## 2743 67.6 71.78753
## 2744 67.6 71.26057
## 2745 67.7 70.48148
## 2746 67.5 70.81644
## 2747 77.1 75.71877
## 2748 76.9 77.66175
## 2749 76.7 73.66242
## 2750 76.5 78.59751
## 2751 76.3 75.43556
## 2752 76.2 75.35182
## 2753 76.0 75.27223
## 2754 75.8 77.10225
## 2755 75.6 76.73252
## 2756 75.4 76.59464
## 2757 75.3 76.23419
## 2758 75.1 75.84386
## 2759 74.9 74.10077
## 2760 74.7 76.76732
## 2761 74.5 75.19873
## 2762 74.2 74.90035
## 2763 81.2 82.29360
## 2764 81.0 82.09664
## 2765 87.0 82.72755
## 2766 86.0 82.45962
## 2767 86.0 81.61136
## 2768 82.0 82.04951
## 2769 81.0 82.25451
## 2770 79.6 82.82571
## 2771 79.5 84.06430
## 2772 79.3 82.02273
## 2773 79.0 78.57717
## 2774 78.8 78.13549
## 2775 78.3 80.83331
## 2776 78.2 81.39110
## 2777 78.0 79.70910
## 2778 77.8 79.61191
## 2779 61.8 65.00993
## 2780 67.0 69.44566
## 2781 59.7 62.93047
## 2782 58.6 61.52239
## 2783 58.3 58.97841
## 2784 57.5 64.08974
## 2785 56.9 55.12295
## 2786 56.2 56.18969
## 2787 54.5 53.69256
## 2788 53.1 53.57208
## 2789 52.2 49.23853
## 2790 51.5 54.96892
## 2791 58.0 50.37235
## 2792 52.0 59.10981
## 2793 49.6 56.58835
## 2794 49.2 49.99795
## 2795 79.3 83.33307
## 2796 79.1 80.77121
## 2797 78.9 81.35467
## 2798 78.8 80.56111
## 2799 78.7 82.51971
## 2800 78.7 81.20597
## 2801 78.5 81.57364
## 2802 78.2 80.48049
## 2803 78.1 81.51717
## 2804 77.8 79.40264
## 2805 77.5 78.23872
## 2806 77.5 79.32635
## 2807 77.2 78.95135
## 2808 77.0 77.16557
## 2809 76.9 74.23293
## 2810 76.8 73.72361
## 2811 77.0 77.66880
## 2812 76.8 77.59992
## 2813 76.8 77.57136
## 2814 76.5 76.77118
## 2815 77.0 77.44149
## 2816 76.3 77.24814
## 2817 76.6 75.05215
## 2818 76.4 74.69525
## 2819 75.4 76.12006
## 2820 76.2 76.54463
## 2821 75.7 76.37080
## 2822 75.4 76.53247
## 2823 75.4 75.82472
## 2824 75.4 75.38663
## 2825 75.2 75.24578
## 2826 75.1 74.02310
## 2827 69.4 71.43112
## 2828 69.2 71.22383
## 2829 69.1 71.06073
## 2830 68.8 70.99733
## 2831 68.5 70.93319
## 2832 68.3 69.40162
## 2833 68.0 69.29010
## 2834 67.9 70.46429
## 2835 67.8 70.24019
## 2836 67.6 70.11961
## 2837 67.3 69.87465
## 2838 67.8 69.89464
## 2839 67.2 69.58508
## 2840 67.1 69.28826
## 2841 67.4 68.99224
## 2842 67.1 64.43630
## 2843 72.0 70.71784
## 2844 71.7 68.58311
## 2845 71.6 68.43386
## 2846 71.4 66.70706
## 2847 71.2 68.26308
## 2848 71.0 68.18473
## 2849 78.0 67.93751
## 2850 75.0 67.77504
## 2851 73.0 67.63101
## 2852 71.0 67.30822
## 2853 69.9 63.00585
## 2854 69.6 62.99216
## 2855 69.4 62.57924
## 2856 69.3 62.35977
## 2857 69.1 62.19685
## 2858 69.0 64.64516
## 2859 74.1 72.59896
## 2860 73.9 72.39142
## 2861 73.8 72.38618
## 2862 73.7 70.20801
## 2863 73.8 72.05802
## 2864 73.7 72.11060
## 2865 73.6 71.87098
## 2866 73.2 71.25507
## 2867 73.4 70.74990
## 2868 73.6 70.40186
## 2869 73.6 69.73552
## 2870 73.3 69.39352
## 2871 72.4 69.17490
## 2872 73.1 68.72663
## 2873 72.5 68.15328
## 2874 72.5 68.28720
## 2875 76.0 70.93281
## 2876 75.9 70.52026
## 2877 75.7 69.55319
## 2878 75.6 72.39850
## 2879 75.4 69.99990
## 2880 75.2 69.73805
## 2881 75.0 69.46026
## 2882 74.9 69.28154
## 2883 74.7 69.09259
## 2884 74.6 68.82034
## 2885 74.4 68.56944
## 2886 74.2 68.09888
## 2887 74.0 67.83200
## 2888 73.8 66.60234
## 2889 73.6 67.63900
## 2890 73.4 67.27937
## 2891 65.7 63.45242
## 2892 65.4 62.02831
## 2893 65.4 63.34538
## 2894 64.7 63.08494
## 2895 64.6 62.71426
## 2896 64.4 62.64522
## 2897 64.1 62.45907
## 2898 63.8 62.43100
## 2899 63.4 66.25528
## 2900 63.0 62.28339
## 2901 62.6 62.09456
## 2902 62.2 61.71411
## 2903 61.9 61.54815
## 2904 61.5 65.40294
## 2905 61.1 61.26469
## 2906 68.0 60.99697
## 2907 61.8 68.10108
## 2908 61.1 62.99530
## 2909 63.0 62.36775
## 2910 59.2 61.39485
## 2911 58.2 60.14202
## 2912 58.0 58.99516
## 2913 57.4 60.15632
## 2914 55.7 62.60483
## 2915 52.6 53.46683
## 2916 58.0 51.47682
## 2917 49.3 50.29597
## 2918 47.9 49.27673
## 2919 46.4 57.84015
## 2920 45.5 56.88280
## 2921 44.6 47.02864
## 2922 43.8 46.47385
## 2923 67.0 59.73936
## 2924 59.2 61.43472
## 2925 58.0 59.69966
## 2926 56.6 57.54467
## 2927 54.9 55.82418
## 2928 52.4 50.72720
## 2929 50.0 48.43725
## 2930 48.2 46.26522
## 2931 46.6 54.59572
## 2932 45.4 54.04709
## 2933 44.6 39.56237
## 2934 44.3 37.79854
## 2935 44.5 36.67575
## 2936 44.8 47.67924
## 2937 45.3 35.44955
## 2938 46.0 34.54925library(Metrics)
data.frame(Method = c("MSE","RMSE","MAE", "MAPE"),
Error.Value = c(mse(predicted, actual),
rmse(predicted, actual),
mae(predicted, actual),
mape(predicted, actual)))## Method Error.Value
## 1 MSE 15.95766123
## 2 RMSE 3.99470415
## 3 MAE 2.97040801
## 4 MAPE 0.04505506range(actual)## [1] 36.3 89.0When compared to the Life.expectancy as the dependent variable’s range, the error values from each technique appear to be tiny. We may therefore anticipate that the predicted values will be fairly close to the actual ones.
plot(actual,col="Red")
lines(actual,col="Red")
plot(predicted,col="Blue")
lines(predicted,col="Blue")
lines(actual,col="Red")
From the above chart, we can interpret that the predicted values are
close enough to the actual. Therefore, the model is a good fit.
Checking on Assumptions
Normality Test
Ploting Residuals on Histogram
hist(model_backward$residuals, breaks = 20)
The majority of the residuals appear to be distributed in the middle,
suggesting that their distribution is normal. ##### Ploting Residuals on
QQPlot
plot(model_backward, which = 2)
The majority of the residuals collected at the middle line suggest that
their distribution is normal.
Shapiro Test
shapiro.test(model_regs$residuals)##
## Shapiro-Wilk normality test
##
## data: model_regs$residuals
## W = 0.96622, p-value < 2.2e-16Based on Shapiro-Wilk normality test, the p-value < 0.05 implying that the distribution of the data are significantly different from normal distribution. Therefore, we need to do some adjustment to data.
Remove Outliers
boxplot(life_exp1$Life.expectancy, ylab = "Life Expectancy (Age)") # visual boxplot
outliers_out <- boxplot(life_exp1$Life.expectancy, plot = F)$out # untuk mendaptkan outlier
life_clean <- life_exp1[-which(life_exp1$Life.expectancy %in% outliers_out), ] # remove outlier dari dataLet us see the Boxplot after Outliers taken
boxplot(life_clean$Life.expectancy, ylab = "Life Expectancy (Age)") # visual boxplot
Unfortunately, there are still some Outliers, so we will eliminate all data with Life.expectancy 50 and below.
life_clean1 <- life_clean[life_clean$Life.expectancy > 50, ] # Eliminate all below Age 50
boxplot(life_clean1$Life.expectancy, ylab = "Life Expectancy (Age)")
##### Creating New Model
clean_full <- lm(formula = Life.expectancy ~., data = life_clean1)
clean_none <- lm(formula = Life.expectancy ~1, data = life_clean1)
clean_backward <- step(clean_full, direction = "backward")## Start: AIC=7257.33
## Life.expectancy ~ Adult.Mortality + infant.deaths + Measles +
## BMI + Total.expenditure + HIV.AIDS + GDP + Population + thinness..1.19.years +
## thinness.5.9.years + Income.composition.of.resources + Schooling +
## Developed + Developing + Hepatitis.B_below90 + Hepatitis.B_above90 +
## Polio_below90 + Polio_above90 + Diphtheria_below90 + Diphtheria_above90
##
##
## Step: AIC=7257.33
## Life.expectancy ~ Adult.Mortality + infant.deaths + Measles +
## BMI + Total.expenditure + HIV.AIDS + GDP + Population + thinness..1.19.years +
## thinness.5.9.years + Income.composition.of.resources + Schooling +
## Developed + Developing + Hepatitis.B_below90 + Hepatitis.B_above90 +
## Polio_below90 + Polio_above90 + Diphtheria_below90
##
##
## Step: AIC=7257.33
## Life.expectancy ~ Adult.Mortality + infant.deaths + Measles +
## BMI + Total.expenditure + HIV.AIDS + GDP + Population + thinness..1.19.years +
## thinness.5.9.years + Income.composition.of.resources + Schooling +
## Developed + Developing + Hepatitis.B_below90 + Hepatitis.B_above90 +
## Polio_below90 + Diphtheria_below90
##
##
## Step: AIC=7257.33
## Life.expectancy ~ Adult.Mortality + infant.deaths + Measles +
## BMI + Total.expenditure + HIV.AIDS + GDP + Population + thinness..1.19.years +
## thinness.5.9.years + Income.composition.of.resources + Schooling +
## Developed + Developing + Hepatitis.B_below90 + Polio_below90 +
## Diphtheria_below90
##
##
## Step: AIC=7257.33
## Life.expectancy ~ Adult.Mortality + infant.deaths + Measles +
## BMI + Total.expenditure + HIV.AIDS + GDP + Population + thinness..1.19.years +
## thinness.5.9.years + Income.composition.of.resources + Schooling +
## Developed + Hepatitis.B_below90 + Polio_below90 + Diphtheria_below90
##
## Df Sum of Sq RSS AIC
## - Measles 1 6.0 36722 7255.8
## - Population 1 6.8 36723 7255.9
## - infant.deaths 1 9.4 36725 7256.1
## - thinness.5.9.years 1 10.9 36727 7256.2
## <none> 36716 7257.3
## - Hepatitis.B_below90 1 30.8 36747 7257.7
## - Diphtheria_below90 1 98.5 36814 7262.9
## - thinness..1.19.years 1 104.5 36820 7263.3
## - Developed 1 157.7 36873 7267.4
## - Total.expenditure 1 160.0 36876 7267.6
## - Polio_below90 1 187.6 36903 7269.7
## - BMI 1 495.8 37212 7293.0
## - GDP 1 926.3 37642 7325.4
## - Income.composition.of.resources 1 1733.0 38449 7385.0
## - Schooling 1 4583.9 41300 7586.0
## - Adult.Mortality 1 6319.6 43035 7701.8
## - HIV.AIDS 1 6902.7 43619 7739.6
##
## Step: AIC=7255.79
## Life.expectancy ~ Adult.Mortality + infant.deaths + BMI + Total.expenditure +
## HIV.AIDS + GDP + Population + thinness..1.19.years + thinness.5.9.years +
## Income.composition.of.resources + Schooling + Developed +
## Hepatitis.B_below90 + Polio_below90 + Diphtheria_below90
##
## Df Sum of Sq RSS AIC
## - infant.deaths 1 5.3 36727 7254.2
## - Population 1 7.1 36729 7254.3
## - thinness.5.9.years 1 10.2 36732 7254.6
## <none> 36722 7255.8
## - Hepatitis.B_below90 1 31.1 36753 7256.2
## - Diphtheria_below90 1 100.2 36822 7261.4
## - thinness..1.19.years 1 104.5 36826 7261.8
## - Total.expenditure 1 157.6 36879 7265.8
## - Developed 1 158.0 36880 7265.9
## - Polio_below90 1 185.6 36907 7268.0
## - BMI 1 490.4 37212 7291.1
## - GDP 1 925.7 37647 7323.8
## - Income.composition.of.resources 1 1735.2 38457 7383.6
## - Schooling 1 4578.8 41301 7584.1
## - Adult.Mortality 1 6336.5 43058 7701.3
## - HIV.AIDS 1 6899.4 43621 7737.8
##
## Step: AIC=7254.19
## Life.expectancy ~ Adult.Mortality + BMI + Total.expenditure +
## HIV.AIDS + GDP + Population + thinness..1.19.years + thinness.5.9.years +
## Income.composition.of.resources + Schooling + Developed +
## Hepatitis.B_below90 + Polio_below90 + Diphtheria_below90
##
## Df Sum of Sq RSS AIC
## - Population 1 3.0 36730 7252.4
## - thinness.5.9.years 1 8.8 36736 7252.9
## <none> 36727 7254.2
## - Hepatitis.B_below90 1 30.6 36758 7254.5
## - Diphtheria_below90 1 100.8 36828 7259.9
## - thinness..1.19.years 1 108.1 36835 7260.5
## - Developed 1 155.0 36882 7264.0
## - Total.expenditure 1 156.6 36884 7264.2
## - Polio_below90 1 188.3 36915 7266.6
## - BMI 1 489.3 37216 7289.4
## - GDP 1 925.9 37653 7322.2
## - Income.composition.of.resources 1 1729.9 38457 7381.6
## - Schooling 1 4601.3 41328 7584.0
## - Adult.Mortality 1 6332.9 43060 7699.4
## - HIV.AIDS 1 6902.1 43629 7736.3
##
## Step: AIC=7252.42
## Life.expectancy ~ Adult.Mortality + BMI + Total.expenditure +
## HIV.AIDS + GDP + thinness..1.19.years + thinness.5.9.years +
## Income.composition.of.resources + Schooling + Developed +
## Hepatitis.B_below90 + Polio_below90 + Diphtheria_below90
##
## Df Sum of Sq RSS AIC
## - thinness.5.9.years 1 9.3 36739 7251.1
## <none> 36730 7252.4
## - Hepatitis.B_below90 1 31.1 36761 7252.8
## - Diphtheria_below90 1 101.0 36831 7258.1
## - thinness..1.19.years 1 106.1 36836 7258.5
## - Developed 1 155.6 36886 7262.3
## - Total.expenditure 1 157.0 36887 7262.4
## - Polio_below90 1 187.2 36917 7264.7
## - BMI 1 492.8 37223 7287.9
## - GDP 1 925.2 37655 7320.4
## - Income.composition.of.resources 1 1738.4 38468 7380.4
## - Schooling 1 4610.0 41340 7582.8
## - Adult.Mortality 1 6337.0 43067 7697.8
## - HIV.AIDS 1 6936.5 43667 7736.7
##
## Step: AIC=7251.14
## Life.expectancy ~ Adult.Mortality + BMI + Total.expenditure +
## HIV.AIDS + GDP + thinness..1.19.years + Income.composition.of.resources +
## Schooling + Developed + Hepatitis.B_below90 + Polio_below90 +
## Diphtheria_below90
##
## Df Sum of Sq RSS AIC
## <none> 36739 7251.1
## - Hepatitis.B_below90 1 30.6 36770 7251.5
## - Diphtheria_below90 1 99.0 36838 7256.7
## - Total.expenditure 1 153.8 36893 7260.9
## - Developed 1 154.0 36893 7260.9
## - Polio_below90 1 187.0 36926 7263.4
## - thinness..1.19.years 1 311.8 37051 7272.9
## - BMI 1 483.7 37223 7285.9
## - GDP 1 921.0 37660 7318.7
## - Income.composition.of.resources 1 1744.2 38484 7379.5
## - Schooling 1 4623.3 41363 7582.3
## - Adult.Mortality 1 6329.7 43069 7696.0
## - HIV.AIDS 1 6928.8 43668 7734.8summary(clean_backward)##
## Call:
## lm(formula = Life.expectancy ~ Adult.Mortality + BMI + Total.expenditure +
## HIV.AIDS + GDP + thinness..1.19.years + Income.composition.of.resources +
## Schooling + Developed + Hepatitis.B_below90 + Polio_below90 +
## Diphtheria_below90, data = life_clean1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.1216 -2.1402 -0.1096 2.1557 16.9158
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.003e+01 5.102e-01 117.642 < 2e-16 ***
## Adult.Mortality -1.868e-02 8.507e-04 -21.956 < 2e-16 ***
## BMI 2.708e-02 4.462e-03 6.070 1.46e-09 ***
## Total.expenditure 1.035e-01 3.024e-02 3.423 0.000629 ***
## HIV.AIDS -6.077e-01 2.646e-02 -22.971 < 2e-16 ***
## GDP 5.040e-05 6.017e-06 8.375 < 2e-16 ***
## thinness..1.19.years -9.497e-02 1.949e-02 -4.873 1.16e-06 ***
## Income.composition.of.resources 6.533e+00 5.668e-01 11.525 < 2e-16 ***
## Schooling 7.159e-01 3.815e-02 18.764 < 2e-16 ***
## Developed 7.763e-01 2.267e-01 3.424 0.000625 ***
## Hepatitis.B_below90 3.516e-01 2.302e-01 1.528 0.126706
## Polio_below90 -1.295e+00 3.432e-01 -3.774 0.000164 ***
## Diphtheria_below90 -1.002e+00 3.648e-01 -2.746 0.006076 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.624 on 2798 degrees of freedom
## Multiple R-squared: 0.8162, Adjusted R-squared: 0.8154
## F-statistic: 1035 on 12 and 2798 DF, p-value: < 2.2e-16clean_forward <- step(clean_none, scope = list(lower = clean_none, upper = clean_full) ,direction = "forward")## Start: AIC=11987.99
## Life.expectancy ~ 1
##
## Df Sum of Sq RSS AIC
## + Schooling 1 119434 80402 9430.7
## + Income.composition.of.resources 1 107856 91980 9808.9
## + Adult.Mortality 1 98638 101199 10077.3
## + BMI 1 62281 137556 10940.2
## + Diphtheria_below90 1 59999 139838 10986.4
## + Diphtheria_above90 1 59999 139838 10986.4
## + Polio_below90 1 59855 139982 10989.3
## + Polio_above90 1 59855 139982 10989.3
## + HIV.AIDS 1 56595 143241 11054.0
## + Developed 1 50141 149695 11177.9
## + Developing 1 50141 149695 11177.9
## + thinness..1.19.years 1 49485 150352 11190.2
## + thinness.5.9.years 1 48828 151008 11202.4
## + GDP 1 43164 156672 11305.9
## + Hepatitis.B_below90 1 27042 172794 11581.3
## + Hepatitis.B_above90 1 27042 172794 11581.3
## + Total.expenditure 1 14880 184957 11772.5
## + infant.deaths 1 7696 192140 11879.6
## + Measles 1 3712 196124 11937.3
## + Population 1 374 199462 11984.7
## <none> 199836 11988.0
##
## Step: AIC=9430.7
## Life.expectancy ~ Schooling
##
## Df Sum of Sq RSS AIC
## + Adult.Mortality 1 26227.4 54175 8322.8
## + HIV.AIDS 1 25071.6 55331 8382.2
## + Income.composition.of.resources 1 7411.9 72990 9160.8
## + Polio_below90 1 7162.6 73240 9170.4
## + Polio_above90 1 7162.6 73240 9170.4
## + Diphtheria_below90 1 6606.4 73796 9191.7
## + Diphtheria_above90 1 6606.4 73796 9191.7
## + BMI 1 5542.6 74860 9231.9
## + GDP 1 4143.2 76259 9284.0
## + thinness.5.9.years 1 3984.5 76418 9289.8
## + thinness..1.19.years 1 3724.0 76678 9299.4
## + Hepatitis.B_below90 1 2665.8 77737 9337.9
## + Hepatitis.B_above90 1 2665.8 77737 9337.9
## + Developed 1 2480.5 77922 9344.6
## + Developing 1 2480.5 77922 9344.6
## + Total.expenditure 1 405.3 79997 9418.5
## + infant.deaths 1 256.3 80146 9423.7
## <none> 80402 9430.7
## + Population 1 14.3 80388 9432.2
## + Measles 1 8.0 80394 9432.4
##
## Step: AIC=8322.85
## Life.expectancy ~ Schooling + Adult.Mortality
##
## Df Sum of Sq RSS AIC
## + HIV.AIDS 1 8916.6 45258 7819.3
## + Polio_below90 1 3644.8 50530 8129.1
## + Polio_above90 1 3644.8 50530 8129.1
## + Diphtheria_below90 1 3447.4 50728 8140.0
## + Diphtheria_above90 1 3447.4 50728 8140.0
## + Income.composition.of.resources 1 3416.9 50758 8141.7
## + BMI 1 2228.3 51947 8206.8
## + thinness..1.19.years 1 2079.7 52095 8214.8
## + GDP 1 2070.1 52105 8215.3
## + thinness.5.9.years 1 2028.4 52147 8217.6
## + Hepatitis.B_below90 1 1380.5 52795 8252.3
## + Hepatitis.B_above90 1 1380.5 52795 8252.3
## + Developed 1 1247.6 52927 8259.4
## + Developing 1 1247.6 52927 8259.4
## + infant.deaths 1 279.0 53896 8310.3
## + Total.expenditure 1 245.9 53929 8312.1
## + Measles 1 46.2 54129 8322.4
## <none> 54175 8322.8
## + Population 1 36.9 54138 8322.9
##
## Step: AIC=7819.34
## Life.expectancy ~ Schooling + Adult.Mortality + HIV.AIDS
##
## Df Sum of Sq RSS AIC
## + Income.composition.of.resources 1 3100.23 42158 7621.9
## + GDP 1 2363.60 42895 7670.6
## + Polio_below90 1 2228.05 43030 7679.4
## + Polio_above90 1 2228.05 43030 7679.4
## + Diphtheria_below90 1 2177.42 43081 7682.7
## + Diphtheria_above90 1 2177.42 43081 7682.7
## + BMI 1 1492.13 43766 7727.1
## + thinness..1.19.years 1 1375.84 43883 7734.6
## + thinness.5.9.years 1 1302.06 43956 7739.3
## + Developed 1 1277.73 43981 7740.8
## + Developing 1 1277.73 43981 7740.8
## + Hepatitis.B_below90 1 682.62 44576 7778.6
## + Hepatitis.B_above90 1 682.62 44576 7778.6
## + Total.expenditure 1 512.14 44746 7789.4
## + infant.deaths 1 310.60 44948 7802.0
## + Population 1 60.77 45198 7817.6
## + Measles 1 46.09 45212 7818.5
## <none> 45258 7819.3
##
## Step: AIC=7621.87
## Life.expectancy ~ Schooling + Adult.Mortality + HIV.AIDS + Income.composition.of.resources
##
## Df Sum of Sq RSS AIC
## + Polio_below90 1 1873.96 40284 7496.1
## + Polio_above90 1 1873.96 40284 7496.1
## + Diphtheria_below90 1 1786.80 40371 7502.1
## + Diphtheria_above90 1 1786.80 40371 7502.1
## + GDP 1 1631.40 40527 7512.9
## + thinness..1.19.years 1 1154.14 41004 7545.8
## + BMI 1 1113.22 41045 7548.7
## + thinness.5.9.years 1 1104.23 41054 7549.3
## + Developed 1 890.66 41268 7563.9
## + Developing 1 890.66 41268 7563.9
## + Total.expenditure 1 635.80 41522 7581.2
## + Hepatitis.B_below90 1 566.00 41592 7585.9
## + Hepatitis.B_above90 1 566.00 41592 7585.9
## + infant.deaths 1 378.22 41780 7598.5
## + Population 1 82.36 42076 7618.4
## + Measles 1 67.12 42091 7619.4
## <none> 42158 7621.9
##
## Step: AIC=7496.06
## Life.expectancy ~ Schooling + Adult.Mortality + HIV.AIDS + Income.composition.of.resources +
## Polio_below90
##
## Df Sum of Sq RSS AIC
## + GDP 1 1530.47 38754 7389.2
## + thinness..1.19.years 1 1178.20 39106 7414.6
## + BMI 1 1077.84 39206 7421.8
## + thinness.5.9.years 1 1056.68 39228 7423.3
## + Developed 1 828.58 39456 7439.6
## + Developing 1 828.58 39456 7439.6
## + Total.expenditure 1 579.58 39705 7457.3
## + infant.deaths 1 192.43 40092 7484.6
## + Hepatitis.B_below90 1 102.47 40182 7490.9
## + Hepatitis.B_above90 1 102.47 40182 7490.9
## + Diphtheria_below90 1 85.09 40199 7492.1
## + Diphtheria_above90 1 85.09 40199 7492.1
## + Population 1 38.20 40246 7495.4
## <none> 40284 7496.1
## + Measles 1 21.47 40263 7496.6
##
## Step: AIC=7389.19
## Life.expectancy ~ Schooling + Adult.Mortality + HIV.AIDS + Income.composition.of.resources +
## Polio_below90 + GDP
##
## Df Sum of Sq RSS AIC
## + thinness..1.19.years 1 1008.11 37746 7317.1
## + BMI 1 998.77 37755 7317.8
## + thinness.5.9.years 1 875.17 37879 7327.0
## + Total.expenditure 1 541.92 38212 7351.6
## + Developed 1 338.06 38416 7366.6
## + Developing 1 338.06 38416 7366.6
## + infant.deaths 1 175.47 38578 7378.4
## + Diphtheria_below90 1 81.70 38672 7385.3
## + Diphtheria_above90 1 81.70 38672 7385.3
## + Population 1 30.19 38724 7389.0
## <none> 38754 7389.2
## + Measles 1 19.84 38734 7389.7
## + Hepatitis.B_below90 1 17.26 38736 7389.9
## + Hepatitis.B_above90 1 17.26 38736 7389.9
##
## Step: AIC=7317.09
## Life.expectancy ~ Schooling + Adult.Mortality + HIV.AIDS + Income.composition.of.resources +
## Polio_below90 + GDP + thinness..1.19.years
##
## Df Sum of Sq RSS AIC
## + BMI 1 480.84 37265 7283.1
## + Total.expenditure 1 301.93 37444 7296.5
## + Developed 1 213.21 37532 7303.2
## + Developing 1 213.21 37532 7303.2
## + Diphtheria_below90 1 77.36 37668 7313.3
## + Diphtheria_above90 1 77.36 37668 7313.3
## <none> 37746 7317.1
## + Hepatitis.B_below90 1 11.34 37734 7318.2
## + Hepatitis.B_above90 1 11.34 37734 7318.2
## + Population 1 8.98 37737 7318.4
## + thinness.5.9.years 1 1.00 37745 7319.0
## + Measles 1 0.65 37745 7319.0
## + infant.deaths 1 0.54 37745 7319.1
##
## Step: AIC=7283.06
## Life.expectancy ~ Schooling + Adult.Mortality + HIV.AIDS + Income.composition.of.resources +
## Polio_below90 + GDP + thinness..1.19.years + BMI
##
## Df Sum of Sq RSS AIC
## + Developed 1 251.493 37013 7266.0
## + Developing 1 251.493 37013 7266.0
## + Total.expenditure 1 251.346 37013 7266.0
## + Diphtheria_below90 1 88.570 37176 7278.4
## + Diphtheria_above90 1 88.570 37176 7278.4
## <none> 37265 7283.1
## + Hepatitis.B_below90 1 13.474 37251 7284.0
## + Hepatitis.B_above90 1 13.474 37251 7284.0
## + Population 1 5.415 37259 7284.6
## + Measles 1 4.530 37260 7284.7
## + thinness.5.9.years 1 2.353 37262 7284.9
## + infant.deaths 1 0.202 37265 7285.0
##
## Step: AIC=7266.02
## Life.expectancy ~ Schooling + Adult.Mortality + HIV.AIDS + Income.composition.of.resources +
## Polio_below90 + GDP + thinness..1.19.years + BMI + Developed
##
## Df Sum of Sq RSS AIC
## + Total.expenditure 1 171.229 36842 7255.0
## + Diphtheria_below90 1 83.869 36929 7261.6
## + Diphtheria_above90 1 83.869 36929 7261.6
## <none> 37013 7266.0
## + Hepatitis.B_below90 1 4.590 37009 7267.7
## + Hepatitis.B_above90 1 4.590 37009 7267.7
## + thinness.5.9.years 1 4.322 37009 7267.7
## + Population 1 4.175 37009 7267.7
## + Measles 1 2.774 37011 7267.8
## + infant.deaths 1 0.363 37013 7268.0
##
## Step: AIC=7254.99
## Life.expectancy ~ Schooling + Adult.Mortality + HIV.AIDS + Income.composition.of.resources +
## Polio_below90 + GDP + thinness..1.19.years + BMI + Developed +
## Total.expenditure
##
## Df Sum of Sq RSS AIC
## + Diphtheria_below90 1 72.073 36770 7251.5
## + Diphtheria_above90 1 72.073 36770 7251.5
## <none> 36842 7255.0
## + thinness.5.9.years 1 7.332 36835 7256.4
## + Measles 1 4.238 36838 7256.7
## + Population 1 3.848 36838 7256.7
## + Hepatitis.B_below90 1 3.722 36838 7256.7
## + Hepatitis.B_above90 1 3.722 36838 7256.7
## + infant.deaths 1 0.614 36841 7256.9
##
## Step: AIC=7251.48
## Life.expectancy ~ Schooling + Adult.Mortality + HIV.AIDS + Income.composition.of.resources +
## Polio_below90 + GDP + thinness..1.19.years + BMI + Developed +
## Total.expenditure + Diphtheria_below90
##
## Df Sum of Sq RSS AIC
## + Hepatitis.B_below90 1 30.6442 36739 7251.1
## + Hepatitis.B_above90 1 30.6442 36739 7251.1
## <none> 36770 7251.5
## + thinness.5.9.years 1 8.8795 36761 7252.8
## + Population 1 4.0503 36766 7253.2
## + Measles 1 3.7115 36766 7253.2
## + infant.deaths 1 0.3162 36770 7253.5
##
## Step: AIC=7251.14
## Life.expectancy ~ Schooling + Adult.Mortality + HIV.AIDS + Income.composition.of.resources +
## Polio_below90 + GDP + thinness..1.19.years + BMI + Developed +
## Total.expenditure + Diphtheria_below90 + Hepatitis.B_below90
##
## Df Sum of Sq RSS AIC
## <none> 36739 7251.1
## + thinness.5.9.years 1 9.3312 36730 7252.4
## + Population 1 3.5451 36736 7252.9
## + Measles 1 3.2099 36736 7252.9
## + infant.deaths 1 0.5214 36739 7253.1summary(clean_forward)##
## Call:
## lm(formula = Life.expectancy ~ Schooling + Adult.Mortality +
## HIV.AIDS + Income.composition.of.resources + Polio_below90 +
## GDP + thinness..1.19.years + BMI + Developed + Total.expenditure +
## Diphtheria_below90 + Hepatitis.B_below90, data = life_clean1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.1216 -2.1402 -0.1096 2.1557 16.9158
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.003e+01 5.102e-01 117.642 < 2e-16 ***
## Schooling 7.159e-01 3.815e-02 18.764 < 2e-16 ***
## Adult.Mortality -1.868e-02 8.507e-04 -21.956 < 2e-16 ***
## HIV.AIDS -6.077e-01 2.646e-02 -22.971 < 2e-16 ***
## Income.composition.of.resources 6.533e+00 5.668e-01 11.525 < 2e-16 ***
## Polio_below90 -1.295e+00 3.432e-01 -3.774 0.000164 ***
## GDP 5.040e-05 6.017e-06 8.375 < 2e-16 ***
## thinness..1.19.years -9.497e-02 1.949e-02 -4.873 1.16e-06 ***
## BMI 2.708e-02 4.462e-03 6.070 1.46e-09 ***
## Developed 7.763e-01 2.267e-01 3.424 0.000625 ***
## Total.expenditure 1.035e-01 3.024e-02 3.423 0.000629 ***
## Diphtheria_below90 -1.002e+00 3.648e-01 -2.746 0.006076 **
## Hepatitis.B_below90 3.516e-01 2.302e-01 1.528 0.126706
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.624 on 2798 degrees of freedom
## Multiple R-squared: 0.8162, Adjusted R-squared: 0.8154
## F-statistic: 1035 on 12 and 2798 DF, p-value: < 2.2e-16Unfortunately, the adj. R-squared significantly decreased from 0.823 to 0.8154. This is not what we anticipated. We will therefore maintain the original data source along with any outliers.
Transform the Data
Let’s attempt to use Log to alter the data. We will only use the model’s internal variables as we have previously determined that “model backward” fits the data the best.
log_life <- lm(formula = log1p(Life.expectancy) ~ log1p(Adult.Mortality) + log1p(Measles) + log1p(BMI) +log1p(Total.expenditure) + log1p(HIV.AIDS) + log1p(GDP) + log1p(thinness..1.19.years) +
log1p(Income.composition.of.resources) + log1p(Schooling) + log1p(Developed) +
log1p(Polio_below90) + log1p(Diphtheria_below90), data = life_exp1)
summary(log_life)##
## Call:
## lm(formula = log1p(Life.expectancy) ~ log1p(Adult.Mortality) +
## log1p(Measles) + log1p(BMI) + log1p(Total.expenditure) +
## log1p(HIV.AIDS) + log1p(GDP) + log1p(thinness..1.19.years) +
## log1p(Income.composition.of.resources) + log1p(Schooling) +
## log1p(Developed) + log1p(Polio_below90) + log1p(Diphtheria_below90),
## data = life_exp1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.50957 -0.03026 0.00100 0.03204 0.23753
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.1002713 0.0148532 276.053 < 2e-16
## log1p(Adult.Mortality) -0.0100412 0.0011572 -8.677 < 2e-16
## log1p(Measles) -0.0030335 0.0003680 -8.243 2.50e-16
## log1p(BMI) 0.0048344 0.0016750 2.886 0.00393
## log1p(Total.expenditure) 0.0044435 0.0030113 1.476 0.14016
## log1p(HIV.AIDS) -0.0953165 0.0017230 -55.321 < 2e-16
## log1p(GDP) 0.0105913 0.0007734 13.694 < 2e-16
## log1p(thinness..1.19.years) -0.0133416 0.0020399 -6.540 7.21e-11
## log1p(Income.composition.of.resources) 0.1684808 0.0118894 14.171 < 2e-16
## log1p(Schooling) 0.0374174 0.0042277 8.850 < 2e-16
## log1p(Developed) 0.0310823 0.0051193 6.072 1.43e-09
## log1p(Polio_below90) -0.0199477 0.0078016 -2.557 0.01061
## log1p(Diphtheria_below90) -0.0236010 0.0077920 -3.029 0.00248
##
## (Intercept) ***
## log1p(Adult.Mortality) ***
## log1p(Measles) ***
## log1p(BMI) **
## log1p(Total.expenditure)
## log1p(HIV.AIDS) ***
## log1p(GDP) ***
## log1p(thinness..1.19.years) ***
## log1p(Income.composition.of.resources) ***
## log1p(Schooling) ***
## log1p(Developed) ***
## log1p(Polio_below90) *
## log1p(Diphtheria_below90) **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.05847 on 2925 degrees of freedom
## Multiple R-squared: 0.8372, Adjusted R-squared: 0.8366
## F-statistic: 1254 on 12 and 2925 DF, p-value: < 2.2e-16The Adj. R-Squared is even larger than the “model backward,” which is good.
bc <- MASS::boxcox(model_backward) # boxcox the model_backward
lambda <- bc$x[which.max(bc$y)] # choose the best lambda
powerTransform <- function(y, lambda1, lambda2 = NULL, method = "boxcox") {
boxcoxTrans <- function(x, lam1, lam2 = NULL) {
# if we set lambda2 to zero, it becomes the one parameter transformation
lam2 <- ifelse(is.null(lam2), 0, lam2)
if (lam1 == 0L) {
log(y + lam2)
} else {
(((y + lam2)^lam1) - 1) / lam1
}
}
switch(method
, boxcox = boxcoxTrans(y, lambda1, lambda2)
, tukey = y^lambda1
)
}
boxcox_life <- lm(powerTransform(Life.expectancy, lambda) ~ Adult.Mortality + Measles + BMI +
Total.expenditure + HIV.AIDS + GDP + thinness..1.19.years +
Income.composition.of.resources + Schooling + Developed +
Polio_below90 + Diphtheria_below90, data = life_exp1)
summary(boxcox_life)##
## Call:
## lm(formula = powerTransform(Life.expectancy, lambda) ~ Adult.Mortality +
## Measles + BMI + Total.expenditure + HIV.AIDS + GDP + thinness..1.19.years +
## Income.composition.of.resources + Schooling + Developed +
## Polio_below90 + Diphtheria_below90, data = life_exp1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1149.6 -161.1 -6.4 162.2 1245.7
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.696e+03 3.538e+01 47.930 < 2e-16 ***
## Adult.Mortality -1.175e+00 5.288e-02 -22.228 < 2e-16 ***
## Measles -8.590e-04 4.467e-04 -1.923 0.05457 .
## BMI 2.166e+00 3.266e-01 6.634 3.88e-11 ***
## Total.expenditure 5.698e+00 2.169e+00 2.627 0.00866 **
## HIV.AIDS -2.738e+01 1.160e+00 -23.611 < 2e-16 ***
## GDP 4.209e-03 4.395e-04 9.577 < 2e-16 ***
## thinness..1.19.years -6.261e+00 1.416e+00 -4.422 1.02e-05 ***
## Income.composition.of.resources 4.944e+02 4.123e+01 11.994 < 2e-16 ***
## Schooling 5.159e+01 2.753e+00 18.740 < 2e-16 ***
## Developed 8.503e+01 1.660e+01 5.122 3.23e-07 ***
## Polio_below90 -9.153e+01 2.466e+01 -3.712 0.00021 ***
## Diphtheria_below90 -6.222e+01 2.474e+01 -2.515 0.01196 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 267.5 on 2925 degrees of freedom
## Multiple R-squared: 0.8216, Adjusted R-squared: 0.8209
## F-statistic: 1123 on 12 and 2925 DF, p-value: < 2.2e-16The Adj. R-Squared is smaller than the “model_backward”, we will not consider the box-cox transformation, and will use log transformation as our new model.
Second Normality Test
Plot Residuals on Histogram
hist(log_life$residuals, breaks = 20)
The Residuals seems has a better distribution at center.
Plot Residuals on QQPlot
plot(log_life, which = 2)
The residuals under -2 and over 2 fell way above/below the center line.
Seems still not following the normal distribution.
Shapiro Test
library(olsrr)
ols_test_normality(log_life)## -----------------------------------------------
## Test Statistic pvalue
## -----------------------------------------------
## Shapiro-Wilk 0.9554 0.0000
## Kolmogorov-Smirnov 0.055 0.0000
## Cramer-von Mises 876.6773 0.0000
## Anderson-Darling 17.1011 0.0000
## -----------------------------------------------Based on Shapiro-Wilk, Kolmogorov-Smirnov, Cramer-von Mises, and Anderson-Darling normality test, the p-value < 0.05 implying that the distribution of the data are significantly different from normal distribution. Therefore, we need to do some adjustment to data.
Homoscedasticity
Plot Fitted vs Residuals
par(mfrow=c(2,1))
plot(log_life, which = c(1:4))
The error seems not following particular pattern, by visual plot
analysis.
Breusch-Pagan Test
library(lmtest)
bptest(log_life)##
## studentized Breusch-Pagan test
##
## data: log_life
## BP = 188.84, df = 12, p-value < 2.2e-16ols_test_breusch_pagan(log_life)##
## Breusch Pagan Test for Heteroskedasticity
## -----------------------------------------
## Ho: the variance is constant
## Ha: the variance is not constant
##
## Data
## --------------------------------------------------
## Response : log1p(Life.expectancy)
## Variables: fitted values of log1p(Life.expectancy)
##
## Test Summary
## -------------------------------
## DF = 1
## Chi2 = 344.8674
## Prob > Chi2 = 5.557104e-77Using 2 different function to test the homocedasticity, we still get conclusion that the residuals variance is not constant.
Multicollinearity Test
vif(log_life)## log1p(Adult.Mortality) log1p(Measles)
## 1.234068 1.235571
## log1p(BMI) log1p(Total.expenditure)
## 1.364789 1.148442
## log1p(HIV.AIDS) log1p(GDP)
## 1.495744 1.693346
## log1p(thinness..1.19.years) log1p(Income.composition.of.resources)
## 1.817267 2.600192
## log1p(Schooling) log1p(Developed)
## 2.234320 1.556913
## log1p(Polio_below90) log1p(Diphtheria_below90)
## 6.139776 6.142181Given that the results of the vif test are less than 10, we may conclude that there is no correlation between any of the independent variables.
Since there is no p-value greater than 0.05, all chosen variables exhibit linear correlation with the dependent variable.
Conclusion
Based on the Adjusted R-Squared value, Error Value, and Pass 2 of 4 Assumption Check, which is the Multicollinearity and Linearity Test, the linear model appears to be able to predict Life Expectancy. However, homocedasticity and normality do not produce the desired outcome. Even though the residuals plot appears to follow the homocedasticity and normal distribution principles when viewed visually, the results of the statistical test are different.
The linear association between Life Expectancy and the chosen independent variables can be explained using the linear model. It is strongly advised to look at the outliers pattern if we still want to apply this model on the new set of Life.expectancy data because it is highly sensitive to outliers (which pretty massively occurred in this data and taking it out is not a smart option).